Real-Time Object Recognition Using a Webcam and Deep Learning

*** This tutorial is two years old and may no longer work properly. You can find an updated tutorial for object recognition at this link***

In this tutorial, we will develop a program that can recognize objects in a real-time video stream on a built-in laptop webcam using deep learning.

object-detection-recognition-video-demo

Object recognition involves two main tasks:

  1. Object Detection (Where are the objects?): Locate objects in a photo or video frame
  2. Image Classification (What are the objects?): Predict the type of each object in a photo or video frame

Humans can do both tasks effortlessly, but computers cannot.

Computers require a lot of processing power to take full advantage of the state-of-the-art algorithms that enable object recognition in real time. However, in recent years, the technology has matured, and real-time object recognition is now possible with only a laptop computer and a webcam.

Real-time object recognition systems are currently being used in a number of real-world applications, including the following:

  • Self-driving cars: detection of pedestrians, cars, traffic lights, bicycles, motorcycles, trees, sidewalks, etc.
  • Surveillance: catching thieves, counting people, identifying suspicious behavior, child detection.
  • Traffic monitoring: identifying traffic jams, catching drivers that are breaking the speed limit.
  • Security: face detection, identity verification on a smartphone.
  • Robotics: robotic surgery, agriculture, household chores, warehouses, autonomous delivery.
  • Sports: ball tracking in baseball, golf, and football.
  • Agriculture: disease detection in fruits.
  • Food: food identification.

There are a lot of steps in this tutorial. Have fun, be patient, and be persistent. Don’t give up! If something doesn’t work the first time around, try again. You will learn a lot more by fighting through to the end of this project. Stay relentless!

By the end of this tutorial, you will have the rock-solid confidence to detect and recognize objects in real time on your laptop’s GPU (Graphics Processing Unit) using deep learning.

Let’s get started!

Table of Contents

You Will Need

Install TensorFlow CPU

We need to get all the required software set up on our computer. I will be following this really helpful tutorial.

Open an Anaconda command prompt terminal.

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Type the command below to create a virtual environment named tensorflow_cpu that has Python 3.6 installed. 

conda create -n tensorflow_cpu pip python=3.6

Press y and then ENTER.

A virtual environment is like an independent Python workspace which has its own set of libraries and Python version installed. For example, you might have a project that needs to run using an older version of Python, like Python 2.7. You might have another project that requires Python 3.7. You can create separate virtual environments for these projects.

Now, let’s activate the virtual environment by using this command:

conda activate tensorflow_cpu
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Type the following command to install TensorFlow CPU.

pip install --ignore-installed --upgrade tensorflow==1.9

Wait for Tensorflow CPU to finish installing. Once it is finished installing, launch Python by typing the following command:

python
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Type:

import tensorflow as tf

Here is what my screen looks like now:

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Now type the following:

hello = tf.constant('Hello, TensorFlow!')
sess = tf.Session()

You should see a message that says: “Your CPU supports instructions that this TensorFlow binary….”. Just ignore that. Your TensorFlow will still run fine.

Now run this command to complete the test of the installation:

print(sess.run(hello))
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Press CTRL+Z. Then press ENTER to exit.

Type:

exit

That’s it for TensorFlow CPU. Now let’s install TensorFlow GPU.

Return to Table of Contents

Install TensorFlow GPU

Your system must have the following requirements:

  • Nvidia GPU (GTX 650 or newer…I’ll show you later how to find out what Nvidia GPU version is in your computer)
  • CUDA Toolkit v9.0 (we will install this later in this tutorial)
  • CuDNN v7.0.5 (we will install this later in this tutorial)
  • Anaconda with Python 3.7+

Here is a good tutorial that walks through the installation, but I’ll outline all the steps below.

Install CUDA Toolkit v9.0

The first thing we need to do is to install the CUDA Toolkit v9.0. Go to this link.

Select your operating system. In my case, I will select Windows, x86_64, Version 10, and exe (local).

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Download the Base Installer as well as all the patches. I downloaded all these files to my Desktop. It will take a while to download, so just wait while your computer downloads everything.

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Open the folder where the downloads were saved to.

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Double-click on the Base Installer program, the largest of the files that you downloaded from the website.

Click Yes to allow the program to make changes to your device.

Click OK to extract the files to your computer.

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I saw this error window. Just click Continue.

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Click Agree and Continue.

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If you saw that error window earlier… “…you may not be able to run CUDA applications with this driver…,” select the Custom (Advanced) install option and click Next. Otherwise, do the Express installation and follow all the prompts.

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Uncheck the Driver components, PhysX, and Visual Studio Integration options. Then click Next.

Click Next.

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Wait for everything to install.

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Click Close.

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Delete  C:\Program Files\NVIDIA Corporation\Installer2.

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Double-click on Patch 1.

Click Yes to allow changes to your computer.

Click OK.

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Click Agree and Continue.

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Go to Custom (Advanced) and click Next.

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Click Next.

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Click Close.

The process is the same for Patch 2. Double-click on Patch 2 now.

Click Yes to allow changes to your computer.

Click OK.

Click Agree and Continue.

Go to Custom (Advanced) and click Next.

Click Next.

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Click Close.

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The process is the same for Patch 3. Double-click on Patch 3 now.

Click Yes to allow changes to your computer.

Click OK.

Click Agree and Continue.

Go to Custom (Advanced) and click Next.

Click Next.

Click Close.

The process is the same for Patch 4. Double-click on Patch 4 now.

Click Yes to allow changes to your computer.

Click OK.

Click Agree and Continue.

Go to Custom (Advanced) and click Next.

Click Next.

After you’ve installed Patch 4, your screen should look like this:

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Click Close.

To verify your CUDA installation, go to the command terminal on your computer, and type:

nvcc --version
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Install the NVIDIA CUDA Deep Neural Network library (cuDNN)

Now that we installed the CUDA 9.0 base installer and its four patches, we need to install the NVIDIA CUDA Deep Neural Network library (cuDNN). Official instructions for installing are on this page, but I’ll walk you through the process below.

Go to https://developer.nvidia.com/rdp/cudnn-download

Create a user profile if needed and log in.

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Go to this page: https://developer.nvidia.com/rdp/cudnn-download

Agree to the terms of the cuDNN Software License Agreement.

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We have CUDA 9.0, so we need to click cuDNN v7.6.4 (September 27, 2019), for CUDA 9.0.

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I have Windows 10, so I will download cuDNN Library for Windows 10.

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In my case, the zip file downloaded to my Desktop. I will unzip that zip file now, which will create a new folder of the same name…just without the .zip part. These are your cuDNN files. We’ll come back to these in a second.

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Before we get going, let’s double check what GPU we have. If you are on a Windows machine, search for the “Device Manager.”

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Once you have the Device Manager open, you should see an option near the top for “Display Adapters.” Click the drop-down arrow next to that, and you should see the name of your GPU. Mine is NVIDIA GeForce GTX 1060.

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If you are on Windows, you can also check what NVIDIA graphics driver you have by right-clicking on your Desktop and clicking the NVIDIA Control Panel. My version is 430.86. This version fits the requirements for cuDNN.

Ok, now that we have verified that our system meets the requirements, lets navigate to C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v9.0, your CUDA Toolkit directory.

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Now go to your cuDNN files, that new folder that was created when you did the unzipping. Inside that folder, you should see a folder named cuda. Click on it.

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Click bin.

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Copy cudnn64_7.dll to C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v9.0\bin. Your computer might ask you to allow Administrative Privileges. Just click Continue when you see that prompt.

Now go back to your cuDNN files. Inside the cuda folder, click on include. You should see a file named cudnn.h.

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Copy that file to C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v9.0\include. Your computer might ask you to allow Administrative Privileges. Just click Continue when you see that prompt.

Now go back to your cuDNN files. Inside the cuda folder, click on lib -> x64. You should see a file named cudnn.lib. 

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Copy that file to C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v9.0\lib\x64. Your computer might ask you to allow Administrative Privileges. Just click Continue when you see that prompt.

If you are using Windows, do a search on your computer for Environment Variables. An option should pop up to allow you to edit the Environment Variables on your computer.

Click on Environment Variables.

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Make sure you CUDA_PATH variable is set to C:\Program Files\NVIDIA GPU Computing Toolkit\CUDA\v9.0.

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I recommend restarting your computer now.

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Install TensorFlow GPU

Now we need to install TensorFlow GPU. Open a new Anaconda terminal window. 

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Create a new Conda virtual environment named tensorflow_gpu by typing this command:

conda create -n tensorflow_gpu pip python=3.6

Type y and press Enter.

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Activate the virtual environment.

conda activate tensorflow_gpu
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Install TensorFlow GPU for Python.

pip install --ignore-installed --upgrade tensorflow-gpu==1.9

Wait for TensorFlow GPU to install.

Now let’s test the installation. Launch the Python interpreter.

python

Type this command.

import tensorflow as tf

If you don’t see an error, TensorFlow GPU is successfully installed.

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Now type this:

hello = tf.constant('Hello, TensorFlow!')
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And run this command. It might take a few minutes to run, so just wait until it finishes:

sess = tf.Session()
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Now type this command to complete the test of the installation:

print(sess.run(hello))
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You can further confirm whether TensorFlow can access the GPU, by typing the following into the Python interpreter (just copy and paste into the terminal window while the Python interpreter is running).

tf.test.is_gpu_available(
    cuda_only=True,
    min_cuda_compute_capability=None
)
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To exit the Python interpreter, type:

exit()
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And press Enter.

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Install TensorFlow Models

Now that we have everything setup, let’s install some useful libraries. I will show you the steps for doing this in my TensorFlow GPU virtual environment, but the steps are the same for the TensorFlow CPU virtual environment.

Open a new Anaconda terminal window. Let’s take a look at the list of virtual environments that we can activate.

conda env list
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I’m going to activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

Install the libraries. Type this command:

conda install pillow lxml jupyter matplotlib opencv cython

Press y to proceed.

Once that is finished, you need to create a folder somewhere that has the TensorFlow Models  (e.g. C:\Users\addis\Documents\TensorFlow). If you have a D drive, you can also save it there as well.

In your Anaconda terminal window, move to the TensorFlow directory you just created. You will use the cd command to change to that directory. For example:

cd C:\Users\addis\Documents\TensorFlow

Go to the TensorFlow models page on GitHub: https://github.com/tensorflow/models.

Click the button to download the zip file of the repository. It is a large file, so it will take a while to download.

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Move the zip folder to the TensorFlow directory you created earlier and extract the contents.

Rename the extracted folder to models instead of models-master. Your TensorFlow directory hierarchy should look like this:

TensorFlow

  • models
    • official
    • research
    • samples
    • tutorials

Return to Table of Contents

Install Protobuf

Now we need to install Protobuf, which is used by the TensorFlow Object Detection API to configure the training and model parameters.

Go to this page: https://github.com/protocolbuffers/protobuf/releases

Download the latest *-win32.zip release (assuming you are on a Windows machine).

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Create a folder in C:\Program Files named it Google Protobuf.

Extract the contents of the downloaded *-win32.zip, inside C:\Program Files\Google Protobuf

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Search for Environment Variables on your system. A window should pop up that says System Properties.

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Click Environment Variables.

Go down to the Path variable and click Edit.

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Click New.

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Add C:\Program Files\Google Protobuf\bin

You can also add it the Path System variable.

Click OK a few times to close out all the windows.

Open a new Anaconda terminal window.

I’m going to activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your \TensorFlow\models\research\ directory and run the following command:

for /f %i in ('dir /b object_detection\protos\*.proto') do protoc object_detection\protos\%i --python_out=.

Now go back to the Environment Variables on your system. Create a New Environment Variable named PYTHONPATH (if you don’t have one already). Replace C:\Python27amd64 if you don’t have Python installed there. Also, replace <your_path> with the path to your TensorFlow folder.

C:\Python27amd64;C:\<your_path>\TensorFlow\models\research\object_detection
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For example:

C:\Python27amd64;C:\Users\addis\Documents\TensorFlow

Now add these two paths to your PYTHONPATH environment variable:

C:\<your_path>\TensorFlow\models\research\
C:\<your_path>\TensorFlow\models\research\slim

Return to Table of Contents

Install COCO API

Now, we are going to install the COCO API. You don’t need to worry about what this is at this stage. I’ll explain it later.

Download the Visual Studios Build Tools here: Visual C++ 2015 build tools from here: https://go.microsoft.com/fwlink/?LinkId=691126

Choose the default installation.

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After it has installed, restart your computer.

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Open a new Anaconda terminal window.

I’m going to activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your \TensorFlow\models\research\ directory and run the following command to install pycocotools (everything below goes on one line):

pip install git+https://github.com/philferriere/cocoapi.git#subdirectory=PythonAPI
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If it doesn’t work, install git: https://git-scm.com/download/win

Follow all the default settings for installing Git. You will have to click Next several times.

Once you have finished installing Git, run this command (everything goes on one line):

pip install git+https://github.com/philferriere/cocoapi.git#subdirectory=PythonAPI

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Test the Installation

Open a new Anaconda terminal window.

I’m going to activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your \TensorFlow\models\research\object_detection\builders directory and run the following command to test your installation.

python model_builder_test.py

You should see an OK message.

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Install LabelImg

Now we will install LabelImg, a graphical image annotation tool for labeling object bounding boxes in images.

Open a new Anaconda/Command Prompt window.

Create a new virtual environment named labelImg by typing the following command:

conda create -n labelImg

Activate the virtual environment.

conda activate labelImg

Install pyqt.

conda install pyqt=5

Click y to proceed.

Go to your TensorFlow folder, and create a new folder named addons.

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Change to that directory using the cd command.

Type the following command to clone the repository:

git clone https://github.com/tzutalin/labelImg.git

Wait while labelImg downloads.

You should now have a folder named addons\labelImg under your TensorFlow folder.

Type exit to exit the terminal.

Open a new terminal window.

Activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your TensorFlow\addons\labelImg directory.

Type the following commands, one right after the other.

conda install pyqt=5
conda install lxml
pyrcc5 -o libs/resources.py resources.qrc
exit

Test the LabelImg Installation

Open a new terminal window.

Activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your TensorFlow\addons\labelImg directory.

Type the following commands:

python labelImg.py

If you see this window, you have successfully installed LabelImg. Here is a tutorial on how to label your own images. Congratulations!

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Recognize Objects Using Your WebCam

Approach

Note: This section gets really technical. If you know the basics of computer vision and deep learning, it will make sense. Otherwise, it will not. You can skip this section and head straight to the Implementation section if you are not interested in what is going on under the hood of the object recognition application we are developing.

In this project, we use OpenCV and TensorFlow to create a system capable of automatically recognizing objects in a webcam. Each detected object is outlined with a bounding box labeled with the predicted object type as well as a detection score.

The detection score is the probability that a bounding box contains the object of a particular type (e.g. the confidence a model has that an object identified as a “backpack” is actually a backpack).

The particular SSD with Inception v2 model used in this project is the ssd_inception_v2_coco model. The ssd_inception_v2_coco model uses the Single Shot MultiBox Detector (SSD) for its architecture and the Inception v2 framework for feature extraction.

Single Shot MultiBox Detector (SSD)

Most state-of-the-art object detection methods involve the following stages:

  1. Hypothesize bounding boxes 
  2. Resample pixels or features for each box
  3. Apply a classifier

The Single Shot MultiBox Detector (SSD) eliminates the multi-stage process above and performs all object detection computations using just a single deep neural network.

Inception v2

Most state-of-the-art object detection methods based on convolutional neural networks at the time of the invention of Inception v2 added increasingly more convolution layers or neurons per layer in order to achieve greater accuracy. The problem with this approach is that it is computationally expensive and prone to overfitting. The Inception v2 architecture (as well as the Inception v3 architecture) was proposed in order to address these shortcomings.

Rather than stacking multiple kernel filter sizes sequentially within a convolutional neural network, the approach of the inception-based model is to perform a convolution on an input with multiple kernels all operating at the same layer of the network. By factorizing convolutions and using aggressive regularization, the authors were able to improve computational efficiency. Inception v2 factorizes the traditional 7 x 7 convolution into 3 x 3 convolutions.

Szegedy, Vanhoucke, Ioffe, Shlens, & Wojna, (2015) conducted an empirically-based demonstration in their landmark Inception v2 paper, which showed that factorizing convolutions and using aggressive dimensionality reduction can substantially lower computational cost while maintaining accuracy.

Data Set

The ssd_inception_v2_coco model used in this project is pretrained on the Common Objects in Context (COCO) data set (COCO data set), a large-scale data set that contains 1.5 million object instances and more than 200,000 labeled images. The COCO data required 70,000 crowd worker hours to gather, annotate, and organize images of objects in natural environments.

Software Dependencies

The following libraries form the object recognition backbone of the application implemented in this project:

  • OpenCV, a library of programming functions for computer vision.
  • Pillow, a library for manipulating images.
  • Numpy, a library for scientific computing.
  • Matplotlib, a library for creating graphs and visualizations.
  • TensorFlow Object Detection API, an open source framework developed by Google that enables the development, training, and deployment of pre-trained object detection models.

Return to Table of Contents

Implementation

Now to the fun part, we will now recognize objects using our computer webcam.

Copy the following program, and save it to your TensorFlow\models\research\object_detection directory as object_detection_test.py .

# Import all the key libraries
import numpy as np
import os
import six.moves.urllib as urllib
import sys
import tarfile
import tensorflow as tf
import zipfile
import cv2

from collections import defaultdict
from io import StringIO
from matplotlib import pyplot as plt
from PIL import Image
from utils import label_map_util
from utils import visualization_utils as vis_util

# Define the video stream
cap = cv2.VideoCapture(0)  

# Which model are we downloading?
# The models are listed here: https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/detection_model_zoo.md
MODEL_NAME = 'ssd_inception_v2_coco_2018_01_28'
MODEL_FILE = MODEL_NAME + '.tar.gz'
DOWNLOAD_BASE = 'http://download.tensorflow.org/models/object_detection/'

# Path to the frozen detection graph. 
# This is the actual model that is used for the object detection.
PATH_TO_CKPT = MODEL_NAME + '/frozen_inference_graph.pb'

# List of the strings that is used to add the correct label for each box.
PATH_TO_LABELS = os.path.join('data', 'mscoco_label_map.pbtxt')

# Number of classes to detect
NUM_CLASSES = 90

# Download Model
opener = urllib.request.URLopener()
opener.retrieve(DOWNLOAD_BASE + MODEL_FILE, MODEL_FILE)
tar_file = tarfile.open(MODEL_FILE)
for file in tar_file.getmembers():
    file_name = os.path.basename(file.name)
    if 'frozen_inference_graph.pb' in file_name:
        tar_file.extract(file, os.getcwd())

# Load a (frozen) Tensorflow model into memory.
detection_graph = tf.Graph()
with detection_graph.as_default():
    od_graph_def = tf.GraphDef()
    with tf.gfile.GFile(PATH_TO_CKPT, 'rb') as fid:
        serialized_graph = fid.read()
        od_graph_def.ParseFromString(serialized_graph)
        tf.import_graph_def(od_graph_def, name='')

# Loading label map
# Label maps map indices to category names, so that when our convolution network 
# predicts `5`, we know that this corresponds to `airplane`.  Here we use internal 
# utility functions, but anything that returns a dictionary mapping integers to 
# appropriate string labels would be fine
label_map = label_map_util.load_labelmap(PATH_TO_LABELS)
categories = label_map_util.convert_label_map_to_categories(
    label_map, max_num_classes=NUM_CLASSES, use_display_name=True)
category_index = label_map_util.create_category_index(categories)


# Helper code
def load_image_into_numpy_array(image):
    (im_width, im_height) = image.size
    return np.array(image.getdata()).reshape(
        (im_height, im_width, 3)).astype(np.uint8)
	
# Detection
with detection_graph.as_default():
    with tf.Session(graph=detection_graph) as sess:
        while True:

            # Read frame from camera
            ret, image_np = cap.read()
            # Expand dimensions since the model expects images to have shape: [1, None, None, 3]
            image_np_expanded = np.expand_dims(image_np, axis=0)
            # Extract image tensor
            image_tensor = detection_graph.get_tensor_by_name('image_tensor:0')
            # Extract detection boxes
            boxes = detection_graph.get_tensor_by_name('detection_boxes:0')
            # Extract detection scores
            scores = detection_graph.get_tensor_by_name('detection_scores:0')
            # Extract detection classes
            classes = detection_graph.get_tensor_by_name('detection_classes:0')
            # Extract number of detectionsd
            num_detections = detection_graph.get_tensor_by_name(
                'num_detections:0')
            # Actual detection.
            (boxes, scores, classes, num_detections) = sess.run(
                [boxes, scores, classes, num_detections],
                feed_dict={image_tensor: image_np_expanded})
            # Visualization of the results of a detection.
            vis_util.visualize_boxes_and_labels_on_image_array(
                image_np,
                np.squeeze(boxes),
                np.squeeze(classes).astype(np.int32),
                np.squeeze(scores),
                category_index,
                use_normalized_coordinates=True,
                line_thickness=8)

            # Display output
            cv2.imshow('object detection', cv2.resize(image_np, (800, 600)))

            if cv2.waitKey(25) & 0xFF == ord('q'):
                cv2.destroyAllWindows()
                break


print("We are finished! That was fun!")

Open a new terminal window.

Activate the TensorFlow GPU virtual environment.

conda activate tensorflow_gpu

cd into your TensorFlow\models\research\object_detection directory.

At the time of this writing, we need to use Numpy version 1.16.4. Type the following command to see what version of Numpy you have on your system.

pip show numpy

If it is not 1.16.4, execute the following commands:

pip uninstall numpy
pip install numpy==1.16.4

Now run, your program:

python object_detection_test.py

In about 30 to 90 seconds, you should see your webcam power up and object recognition take action. That’s it! Congratulations for making it to the end of this tutorial!

object_detection_resultsJPG

Keep building!

Return to Table of Contents

Value Iteration vs. Q-Learning Algorithm in Python Step-By-Step

In this post, I will walk you through how to implement the value iteration and Q-learning reinforcement learning algorithms from scratch, step-by-step. We will not use any fancy machine learning libraries, only basic Python libraries like Pandas and Numpy.

Our end goal is to implement and compare the performance of the value iteration and Q-learning reinforcement learning algorithms on the racetrack problem (Barto, Bradtke, & Singh, 1995).

In the racetrack problem, the goal is to control the movement of a race car along a predefined racetrack so that the race car travels from the starting position to the finish line in a minimum amount of time. The race car must stay on the racetrack and avoid crashing into walls along the way. The racetrack problem is analogous to a time trial rather than a competitive race since there are no other cars on the track to avoid.

Note: Before you deep dive into a section below, I recommend you check out my introduction to reinforcement learning post so you can familiarize yourself with what reinforcement learning is and how it works. Once you skim over that blog post, the rest of this article will make a lot more sense. If you are already familiar with how reinforcement learning works, no need to read that post. Just keep reading this one.

Without further ado, let’s get started!

Table of Contents

Testable Hypotheses

The two reinforcement learning algorithms implemented in this project were value iteration and Q-learning. Both algorithms were tested on two different racetracks: an R-shaped racetrack and an L-shaped racetrack. The number of timesteps the race car needed to take from the starting position to the finish line was calculated for each algorithm-racetrack combination.

Using the implementations of value iteration and Q-learning, three hypotheses will be tested.

Hypothesis 1: Both Algorithms Will Enable the Car to Finish the Race

I hypothesize that value iteration and Q-learning will both generate policies that will enable the race car to successfully finish the race on all racetracks tested (i.e. move from the starting position of the racetracks to the finish line).

Hypothesis 2: Value Iteration Will Learn Faster Than Q-Learning

I hypothesize that value iteration will generate a learning policy faster than Q-learning because it has access to the transition and reward functions (explained in detail in the next section “Algorithms Implemented”).  

Hypothesis 3: Bad Crash Version 1 Will Outperform Bad Crash Version 2

I hypothesize that it will take longer for the car to finish the race for the crash scenario in which the race car needs to return to the original starting position each time it crashes into a wall. In other words, Bad Crash Version 1 (return to nearest open position) performance will be better than Bad Crash Version 2 (return to start) performance.

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How Value Iteration Works

In the case of the value iteration reinforcement learning algorithm, the race car (i.e. agent) knows two things before taking a specific action (i.e. accelerate in x and/or y directions) (Alpaydin, 2014):

  1. The probabilities of ending up in other new states given a particular action is taken from a current state.
    • More formally, the race car knows the transition function.
    • As discussed in the previous section, the transition function takes as input the current state s and selected action a and outputs the probability of transitioning to some new state s’.
  2. The immediate reward (e.g. race car gets -1 reward each time it moves to a new state) that would be received for taking a particular action from a current state.
    • More formally, this is known as the reward function.
    • The reward function takes as input the current state s and selected action a and outputs the reward.

Value iteration is known as a model-based reinforcement learning technique because it tries to learn a model of the environment where the model has two components:

  1. Transition Function
    • The race car looks at each time it was in a particular state s and took a particular action a and ended up in a new state s’. It then updates the transition function (i.e. transition probabilities) according to these frequency counts.
  2. Reward Function
    • This function answers the question: “Each time the race car was in a particular state s and took a particular action a, what was the reward?”

In short, in value iteration, the race car knows the transition probabilities and reward function (i.e. the model of the environment) and uses that information to govern how the race car should act when in a particular state. Being able to look ahead and calculate the expected rewards of a potential action gives value iteration a distinct advantage over other reinforcement learning algorithms when the set of states is small in size.

Let us take a look at an example. Suppose the following:

  • The race car is in state so, where s0 = <x0, y0, vx0, vy0>, corresponding to the x-position on a racetrack, y-position on a race track, velocity in the x direction, and velocity in the y direction, at timestep 0.
  • The race car takes action a0, where a0 = (ax0, ay0) = (change in velocity in x-direction, change in velocity in y-direction)
  • The race car then observes the new state, where the new state is s1, where s1 = <x1, y1, vx1, vy1>.
  • The race car receives a reward r0 for taking action a0 in state s0.

Putting the bold-faced variables together, we get the following expression which is known as an experience tuple. Tuples are just like lists except the data inside of them cannot be changed.

Experience Tuple = <s0, a0, s1, r0>

What the experience tuple above says is that if the race car is in state s0 and takes action a0, the race car will observe a new state s1 and will receive reward r0.

Then at the next time step, we generate another experience tuple that is represented as follows.

Experience Tuple = <s1, a1, s2, r1>

This process of collecting experience tuples as the race car explores the race track (i.e. environment) happens repeatedly.

Because value iteration is a model based approach, it builds a model of the transition function T[s, a, s’] and reward function R[s,a,s’] using the experience tuples.

  • The transition function can be built and updated by adding up how many times the race car was in state s and took a particular action a and then observed a new state s’. Recall that T[s, a, s’] stands for the probability the race car finds itself in a new state s’ (at the next timestep) given that it was in state s and took action a.
  • The reward function can be built by examining how many times the race car was in state s and took a particular action a and received a reward r. From that information the average reward for that particular scenario can be calculated.

Once these models are built, the race car can then can use value iteration to determine the optimal values of each state (hence the name value iteration). In some texts, values are referred to as utilities (Russell, Norvig, & Davis, 2010).

What are optimal values?

Each state s in the environment (denoted as <xt, yt, vxt, vyt > in this racetrack project) has a value V(s). Different actions can be taken in a given state s. The optimal values of each state s are based on the action a that generates the best expected cumulative reward.

Expected cumulative reward is defined as the immediate reward that the race car would receive if it takes action a and ends up in the state s + the discounted reward that the race car would receive if it always chose the best action (the one that maximizes total reward) from that state onward to the terminal state (i.e. the finish line of the racetrack).

V*(s) = best possible (immediate reward + discounted future reward)

where the * means “optimal.”

The reason why those future rewards are discounted (typically by a number in the range [0,1), known as gamma γ) is because rewards received far into the future are worth less than rewards received immediately. For all we know, the race car might have a gas-powered engine, and there is always the risk of running out of gas. After all, would you rather receive $10 today or $10 ten years from now? $10 received today is worth more (e.g. you can invest it to generate even more cash). Future rewards are more uncertain so that is why we incorporate the discount rate γ.

It is common in control applications to see state-action pairs denoted as Q*(s, a) instead of V*(s) (Alpaydin, 2014). Q*(s,a) is the [optimal] expected cumulative reward when the race car takes an action a in state s and always takes the best action after that timestep. All of these values are typically stored in a table. The table maps state-action pairs to the optimal Q-values (i.e. Q*(s,a)).

Each row in the table corresponds to a state-action-value combination. So in this racetrack problem, we have the following entries into the value table:

[x, y, vx, vy, ax, ay, Q(s,a)] = [x-coordinate, y-coordinate, velocity in x-direction, velocity in y-direction, acceleration in x-direction, acceleration in y-direction, value when taking that action in that state] 

Note that Q(s,a) above is not labeled Q*(s,a). Only once value iteration is done can we label it Q*(s,a) because it takes time to find the optimal Q values for each state-action pair.

With the optimal Q values for each state-action pair, the race car can calculate the best action to take given a state. The best action to take given a state is the one with the highest Q value.

At this stage, the race car is ready to start the engine and leave the starting position.

At each timestep of the race, the race car observes the state (i.e. position and velocity) and decides what action to apply by looking at the value table. It finds the action that corresponds to the highest Q value for that state. The car then takes that action.

The pseudocode for calculating the optimal value for each state-action pair (denoted as Q*(s,a)) in the environment is below. This algorithm is the value iteration algorithm because it iterates over all the state-action pairs in the environment and gives them a value based on the cumulative expected reward of that state-action pair (Alpaydin, 2014; Russell, Norvig, & Davis, 2010; Sutton & Barto, 2018):

Value Iteration Algorithm Pseudocode

Inputs

  • States:
    • List of all possible values of x
    • List of all possible values of y
    • List of all possible values of vx
    • List of all possible values of vy
  • Actions:
    • List of all the possible values of ax
    • List of all possible values of ay
  • Model:
    • Model = Transition Model T[s, a, s’] + Reward Model R[s, a, s’]
    • Where Model is a single table with the following row entries
      • [s, a, s’, probability of ending up in a new state s’ given state s and action a, immediate reward for ending up in new state s’ given state s and action a]
      • = [s, a, s’, T(s, a, s’), R(s, a, s’)]
      • Note that the reward will be -1 for each state except the finish line states (i.e. absorbing or terminal states), which will have a reward of 0.
  • Discount Rate:
    • γ
      • Where 0 ≤ γ < 1
      • If γ = 0, rewards received immediately are the only thing that counts.
      • As γ gets close to 1, rewards received further in the future count more.
  • Error Threshold
    • Ɵ
      • Ɵ is a small number that helps us to determine when we have optimal values for each state-action pair (also known as convergence).
      • Ɵ helps us know when the values of each state-action pair, denoted as Q(s,a), stabilize (i.e. stop changing a lot from run to run of the loop).

Process

  • Create a table V(s) that will store the optimal Q-value for each state. This table will help us determine when we should stop the algorithm and return the output. Initialize all the values of V(s) to arbitrary values, except the terminal state (i.e. finish line state) that has a value of 0.
  • Initialize all Q(s,a) to arbitrary values, except the terminal state (i.e. finish line states) that has a value of 0.
  • Initialize a Boolean variable called done that is a flag to indicate when we are done building the model (or set a fixed number of training iterations using a for loop).
  • While (Not Done)
    • Initialize a value called Δ to 0. When this value gets below the error threshold Ɵ, we exit the main loop and return the output.
    • For all possible states of the environment
      • v := V(s)            // Extract and store the most recent value of the state
      • For all possible actions the race car (agent) can take
        • Q(s,a) = (expected immediate reward given the state s and an action a) + (discount rate) * [summation_over_all_new_states(probability of ending up in a new state s’given a state s and action a * value of the new state s’)]
        • More formally,
          •  
          • where  = expected immediate return when taking action a from state s
      • V(s) := maximum value of Q(s,a) across all the different actions that the race car can take from state s
      • Δ := maximum(Δ, |v – V(s)|)
    • Is Δ < Ɵ? If yes, we are done (because the values of V(s) have converged i.e. stabilized), otherwise we are not done.

Output

The output of the value iteration algorithm is the value table, the table that maps state-action pairs to the optimal Q-values (i.e. Q*(s,a)).

Each row in the table corresponds to a state-action-value combination. So in this racetrack problem, we have the following entries into the value table:

[x, y, vx, vy, ax, ay, Q(s,a)] = [x-coordinate, y-coordinate, velocity in x-direction, velocity in y-direction, acceleration in x-direction, acceleration in y-direction, value when taking that action in that state] 

Policy Determination

With the optimal Q values for each state-action pair, the race car can calculate the best action to take given a state. The best action to take given a state is the one with the highest Q value.

At this stage, the race car is ready to start the engine and leave the starting position.

At each timestep t of the race, the race car observes the state st (i.e. position and velocity) and decides what action at to apply by looking at the value table. It finds the action that corresponds to the highest Q value for that state (the action that will generate the highest expected cumulative reward). The car then takes that action at*, where at* means the optimal action to take at time t.

More formally, the optimal policy for a given states s at timestep t is π*(s) where:

For each state s do

value-iter-policy-equation

Value Iteration Summary

So, to sum up, on a high level, the complete implementation of an autonomous race car using value iteration has two main steps:

  • Step 1: During the training phase, calculate the value of each state-action pair.
  • Step 2: At each timestep of the time trial, given a current state s, select the action a where the state-action pair value (i.e. Q*(s,a)) is the highest.

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How Q-Learning Works

Overview

In most real-world cases, it is not computationally efficient to build a complete model (i.e. transition and reward function) of the environment beforehand.  In these cases, the transition and reward functions are unknown. To solve this issue, model-free reinforcement learning algorithms like Q-learning were invented (Sutton & Barto, 2018) .

In the case of model-free learning, the race car (i.e. agent) has to interact with the environment and learn through trial-and-error. It cannot look ahead to inspect what the value would be if it were to take a particular action from some state. Instead, in Q-learning, the race car builds a table of Q-values denoted as Q(s,a) as it takes an action a from a state s and then receives a reward r. The race car uses the Q-table at each timestep to determine the best action to take given what it has learned in previous timesteps.

One can consider Q[s,a] as a two-dimensional table that has the states s as the rows and the available actions a as the columns. The value in each cell of this table (i.e. the Q-value) represents the value of taking action a in state s.

Just like in value iteration, value has two components, the immediate reward and the discounted future reward.

More formally,

Q[s,a] = immediate reward + discounted future reward

Where immediate reward is the reward you get when taking action a from state s, and discounted future reward is the reward you get for taking actions in the future, discounted by some discount rate γ. The reason why future rewards are discounted is because rewards received immediately are more certain than rewards received far into the future (e.g. $1 received today is worth more than $1 received fifty years from now).

So, how does the race car use the table Q[s,a] to determine what action to take at each timestep of the time trial (i.e. what is the policy given a state…π(s))?

Each time the race car observes state s, it consults the Q[s,a] table. It takes a look to see which action generated the highest Q value given that observed state s. That action is the one that it takes.

More formally,

π(s) = argmaxa(Q[s,a])

argmax is a function that returns the action a that maximizes the expression Q[s,a]. In other words, the race car looks across all position actions given a state and selects the action that has the highest Q-value.

After Q-learning is run a number of times, an optimal policy will eventually be found. The optimal policy is denoted as π*(s). Similarly the optimal Q-value is Q*[s,a].

How the Q[s,a] Table Is Built

Building the Q[s,a] table can be broken down into the following steps:

  1. Choose the environment we want to train on.
    • In this race car problem, the racetrack environment is what we want the race car to explore and train on.
    • The racetrack provides the x and y position data that constitutes a portion of the state s that will be observed at each timestep by the racecar (agent).
  2. Starting from the starting position, the race car moves through the environment, observing the state s at a given timestep
  3. The race car consults the policy π(s), the function that takes as input the current state and outputs an action a.
  4. The action a taken by the race car changes the state of the environment from s to s’. The environment also generates a reward r that is passed to the race car.
  5. Steps 2-4 generate a complete experience tuple (i.e. a tuple is a list that does not change) of the form <s, a, s’, r> = <state, action, new state, reward>.
  6. The experience tuple in 5 is used to update the Q[s,a] table.
  7. Repeat steps 3-6 above until the race car gets to the terminal state (i.e. the finish line of the racetrack).

With the Q[s,a] table built, the race car can now test the policy. Testing the policy means starting at the starting position and consulting the Q[s,a] table at each timestep all the way until the race car reaches the finish line. We count how many timesteps it took for the race car to reach the finish line. If the time it took the race car to complete the time trial is not improving, we are done. Otherwise, we make the race car go back through the training process and test its policy again with an updated Q[s,a] table.

We expect that eventually, the performance of the race car will reach a plateau.

How the Q[s,a] Table Is Updated

With those high level steps, let us take a closer look now at how the Q[s,a] table is updated in step 6 in the previous section.

Each time the race car takes an action, the environment transitions to a new state s’ and gives the race car a reward r. This information is used by the race car to update its Q[s,a] table.

The update rule consists of two parts, where Q’[s,a] is the new updated Q-value for an action a taken at state s.

Q’[s,a] = Q[s,a] + α * (improved estimate of Q[s,a] – Q[s,a])

where α is the learning rate.

The learning rate is a number 0 < α ≤ 1 (commonly 0.2). Thus, the new updated Q-value is a blend of the old Q-value and the improved estimate of the Q value for a given state-action pair. The higher the learning rate, the more new information is considered when updating the Q-value. A learning rate of 1 means that the new updated Q-value is only considering the new information.

The equation above needs to be expanded further.

Q’[s,a] =Q[s,a] + α*(immediate reward + discounted future reward – Q[s,a])

Q’[s,a] = Q[s,a] + α * (r + γ * future reward – Q[s,a])

Where γ is the discount rate. It is typically by a number in the range [0,1). It means that rewards received by the race car (agent) in the far future are worth less than an immediate reward.

Continuing with the expansion of the equation, we have:

Q’[s,a] = Q[s,a] + α * (r + γ * Q[s’, optimal action a’ at new state s’] – Q[s,a])

Note in the above equation that we assume that the race car reaches state s’ and takes the best action from there, where best action is the action a’ that has the highest Q-value for that given new state s’.

More formally the update rule is as follows:

Q’[s,a] = Q[s,a] + α * (r + γ * Q[s’, argmaxa’(Q[s’,a’])] – Q[s,a])

Where argmaxa’(Q[s’,a’]) returns the action a’ that has the highest Q value for a given state s’.

How an Action Is Selected at Each Step

The performance of Q-learning is improved the more the race car explores different states and takes different actions in those states. In other words, the more state-action pairs the race car explores, the better Q[s,a] table the race car is able to build.

One strategy for forcing the race car to explore as much of the state-action space as possible is to add randomness into the Q-learning procedure. This is called exploration. More specifically, at the step of Q-learning where the race car selects an action based on the Q[s,a] table:

  • There is a 20% chance ε that the race car will do some random action, and a 80% chance the race car will do the action with the highest Q-value (as determined by the Q[s,a] table). The latter is known as exploitation.
  • If the race car does some random action, the action is chosen randomly from the set of possible actions the race car can perform.

I chose 20% as the starting probability (i.e. ε) of doing some random action, but it could be another number (e.g. 30%) As the race car gains more experience and the Q[s,a] table gets better and better, we want the race car to take fewer random actions and follow its policy more often. For this reason, it is common to reduce ε with each successive iteration, until we get to a point where the race car stops exploring random actions.

Q-Learning Algorithm Pseudocode

Below are is the Q-learning algorithm pseudocode on a high level (Alpaydin, 2014; Sutton & Barto, 2018).

Inputs

  • Learning rate α, where 0 < α ≤ 1 (e.g. 0.2)
  • Discount rate γ (e.g. 0.9)
  • Exploration probability ε, corresponding to the probability that the race car will take a random action given a state (e.g. 0.2)
  • Reduction of exploration probability, corresponding to how much we want to decrease ε at each training iteration (defined as a complete trip from the starting position to the finish line terminal state) of the Q-learning process. (e.g. 0.5)
  • Number of training iterations (e.g. 1,000,000)
  • States:
    • List of all possible values of x
    • List of all possible values of y
    • List of all possible values of vx
    • List of all possible values of vy
  • Actions:
    • List of all the possible values of ax
    • List of all possible values of ay

Process

  • Initialize the Q[s,a] table to small random values, except for the terminal state which will have a value of 0.
  • For a fixed number of training iterations
    • Initialize the state to the starting position of the race track
    • Initialize a Boolean variable to see if the race car has crossed the finish line (i.e. reached the terminal state)
    • While the race car has not reached the finish line
      • Select the action a using the Q[s,a] table that corresponds to the highest Q value given state s
      • Take action a
      • Observe the reward r and the new state s’
      • Update the Q[s,a] table:
        • Q[s,a] := Q[s,a] + α * (r + γ * Q[s’, argmaxa’(Q[s’,a’])] – Q[s,a])
      • s := s’
      • Check if we have crossed the finish line

Output

Algorithm returns the Q[s,a] table which is used to determine the optimal policy.

Policy Determination

Each time the race car observes state s, it consults the Q[s,a] table. It takes a look to see which action generated the highest Q value given that observed state s. That action is the one that it takes.

More formally,

π(s) = argmaxa(Q[s,a])

argmax is a function that returns the action a that maximizes the expression Q[s,a]. In other words, the race car looks across all position actions given a state and selects the action that has the highest Q-value.

Helpful Video

Here is a good video where Professor Tucker Balch from Georgia Tech goes through Q-learning, step-by-step:

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Experimental Design and Tuning Process

Experimental Design

The Q-learning and value iteration algorithms were implemented for the racetrack problem and then tested on two different racetracks: an R-shaped racetrack and an L-shaped racetrack. The number of timesteps the race car needed to find the finish line was calculated for each algorithm-racetrack combination. The number of training iterations was also monitored. 10 experiments for each algorithm-racetrack combination were performed to create data to graph a learning curve.

At each timestep t of the racetrack problem, we have the following variables (below). We assume the racetrack is a Cartesian grid with an x-axis and a y-axis, and that the system is governed by the standard laws of kinematics:

  • State = <xt, yt, vxt, vyt> = variables that describe the current situation (i.e. environment)
    • xt = x coordinate of the location of the car at timestep t
    • yt = y coordinate of the location of the car at timestep t
    • vxt = velocity in the x direction at time step t, where vxt = xt – xt-1
      • Maximum vxt = 5
      • Minimum vxt = -5
    • vyt = velocity in the y direction at timestep t, where vyt = yt – yt-1
  • Action = <axt, ayt> = control variables = what the race car (i.e. agent) can do to influence the state
    • axt = accelerate in the x direction at timestep t, where axt = vxt  – vx t-1
      • -1 (decrease velocity in x-direction by 1)
      • 0 (keep same velocity), or
      • 1 (increase velocity in x-direction by 1)
    • ayt = acceleration in the y direction at timestep t, where ayt = vyt  – vy t-1
      • -1 (decrease velocity in y-direction by 1)
      • 0 (keep same velocity)
      • 1 (increase velocity in y-direction by 1)

Example Calculation

At t = 0, the race car observes the current state. Location is (2,2) and velocity is (1,0).

  • State = <xt, yt, vxt, vyt> = <x0, y0, vx0, vy0> = <2, 2, 1, 0>
  • This means the race car is moving east one grid square per timestep because the x-component of the velocity is 1, and the y-component is 0.

After observing the state, the race car selects an action. It accelerates with acceleration (1,1).

  • Action=(ax0, ay0)=(1, 1) = (increase velocity in x-direction by 1, increase velocity in y-direction by 1)

At t = 1, the race car observes the state.

  • Velocity is now (vx0 + ax0, vy0 + ay0) = (1 + 1, 0 + 1) = (vx1, vy1) = (2, 1)
  • Position (i.e. x and y coordinates) is now (x0 + vx1, y0 + vy1) = (2 + 2, 2 + 1) = (x1, y1) = (4, 3)
  • Thus, putting it all together, the new state is now <x1, y1, vx1, vy1> = <4, 3, 2, 1>

Acceleration is Not Guaranteed

There is another twist with the racetrack problem. At any timestep t, when the race car attempts to accelerate, there is a 20% chance that the attempt will fail. In other words, each time the race car selects an action, there is a:

  • 20% chance that the attempt fails, and velocity remains unchanged at the next timestep; i.e. (axt, ayt) = (0, 0)
  • 80% chance velocity changes at the next timestep; (axt, ayt) = (selected acceleration in the x-direction, selected acceleration in y-direction)

Must Avoid Crashing Into Walls

The race car must stay on the track. Crashing into walls is bad. Two versions of a “bad crash” will be implemented in this project:

  • Bad Crash Version 1: If the car crashes into a wall,
    • The car is placed at the nearest position on the track to the place where the car crashed.
    • The velocity is set to (0, 0).
  • Bad Crash Version 2: If the car crashes into a wall,
    • The car must go back to the original starting position.
    • The velocity is set to (0, 0).

In this project, the performance of both versions of bad crash will be compared side by side for the reinforcement learning algorithms implemented in this project.

Reward Function

Because the goal is for the race car to go from the starting position to the finish line in the minimum number of timesteps, we assign a reward of -1 for each move the car makes. Because the reward is negative, this means that the race car incurs a cost (i.e. penalty) of 1 each time the race car moves to another position. The goal is to get to the finish line in as few moves (i.e. time steps) as possible in order to minimize the total cost (i.e. maximize the total reward).

The finish line is the final state (often referred to as terminal or absorbing state). This state has a reward of 0. There is no requirement to stop right on the finish position (i.e. finish line). It is sufficient to cross it.

Description of Any Tuning Process Applied

In order to compare the performance of the algorithm for the different crash scenarios, the principal hyperparameters were kept the same for all runs. These hyperparameters are listed below.

Learning Rate

The Learning rate α was set to 0.2.

Discount Rate

The discount rate γ was set to 0.9.

Exploration Probability

The exploration probability ε was set to 0.2 as dictated by the problem statement.

Number of Training Iterations

The number of training iterations was varied in order to computer the learning curve (see Results section below)

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Input Files

Here are the tracks used in this project (S= Starting States; F = Finish States, # = Wall, . = Track):

Value Iteration Code in Python

Here is the full code for value iteration. Don’t be scared by how long this code is. I included a lot of comments so that you know what is going on at each step of the code. This and the racetrack text files above are all you need to run the program (just copy and paste into your favorite IDE!):

import os # Library enables the use of operating system dependent functionality
import time # Library handles time-related tasks
from random import shuffle # Import shuffle() method from the random module
from random import random # Import random() method from the random module
from copy import deepcopy # Enable deep copying
import numpy as np # Import Numpy library

# File name: value_iteration.py
# Author: Addison Sears-Collins
# Date created: 8/14/2019
# Python version: 3.7
# Description: Implementation of the value iteration reinforcement learning
# algorithm for the racetrack problem. 
# The racetrack problem is described in full detail in: 
# Barto, A. G., Bradtke, S. J., Singh, S. P. (1995). Learning to Act Using 
#   Real-time Dynamic Programming. Artificial Intelligence, 72(1-2):81–138.
# and 
# Sutton, Richard S., and Andrew G. Barto. Reinforcement learning : 
#   An Introduction. Cambridge, Massachusetts: The MIT Press, 2018. Print.
#   (modified version of Exercise 5.12 on pg. 111)

# Define constants
ALGORITHM_NAME = "Value_Iteration"
FILENAME = "R-track.txt"
THIS_TRACK = "R_track"
START = 'S'
GOAL = 'F'
WALL = '#'
TRACK = '.'
MAX_VELOCITY = 5
MIN_VELOCITY = -5
DISC_RATE = 0.9  # Discount rate, also known as gamma. Determines by how much
                 # we discount the value of a future state s'
ERROR_THRES = 0.001 # Determine when Q-values stabilize (i.e.theta)
PROB_ACCELER_FAILURE = 0.20 # Probability car will try to take action a 
                            # according to policy pi(s) = a and fail.
PROB_ACCELER_SUCCESS = 1 - PROB_ACCELER_FAILURE
NO_TRAINING_ITERATIONS = 10 # A single training iteration runs through all
                            # possible states s
NO_RACES = 10 # How many times the race car does a single time trial from 
              # starting position to the finish line
FRAME_TIME = 0.3 # How many seconds between frames printed to the console
MAX_STEPS = 500 # Maximum number of steps the car can take during time trial
MAX_TRAIN_ITER = 50 # Maximum number of training iterations

# Range of the velocity of the race car in both y and x directions
vel_range = range(MIN_VELOCITY, MAX_VELOCITY + 1)

# All actions A the race car can take
# (acceleration in y direction, acceleration in x direction)
actions = [(-1,-1), (0,-1), (1,-1),
           (-1,0) , (0,0),  (1,0),
           (-1,1) , (0,1),  (1,1)]

def read_environment(filename):
    """
    This method reads in the environment (i.e. racetrack)
    :param str filename
    :return environment: list of lists
    :rtype list
    """
    # Open the file named filename in READ mode.
    # Make the file an object named 'file'
    with open(filename, 'r') as file:

        # Read until end of file using readline() 
        # readline() then returns a list of the lines
        # of the input file
        environment_data = file.readlines()
    
    # Close the file
    file.close()

    # Initialize an empty list
    environment = []

    # Adds a counter to each line in the environment_data list,
    # i is the index of each line and line is the actual contents.
    # enumerate() helps get not only the line of the environment but also 
    # the index of that line (i.e. row)
    for i,line in enumerate(environment_data):
        # Ignore the first line that contains the dimensions of the racetrack
        if i > 0:
            # Remove leading or trailing whitespace if applicable
            line = line.strip()

            # If the line is empty, ignore it
            if line == "": continue

            # Creates a list of lines. Within each line is a list of 
            # individual characters
            # The stuff inside append(stuff) first creates a new_list = []
            # It then appends all the values in a given line to that new 
            # list (e.g. new_list.append(all values inside the line))
            # Then we append that new list to the environment list.
            # Therefoer, environment is a list of lists.
            environment.append([x for x in line])

    # Return the environment (i.e. a list of lists/lines)
    return environment

def print_environment(environment, car_position = [0,0]):
    """
    This method reads in the environment and current 
    (y,x) position of the car and prints the environment to the console
    :param list environment
    :param list car_position 
    """
    # Store value of current grid square
    temp = environment[car_position[0]][car_position[1]]

    # Move the car to current grid square
    environment[car_position[0]][car_position[1]] = "X"

    # Delay 
    time.sleep(FRAME_TIME)

    # Clear the printed output
    clear()

    # For each line in the environment
    for line in environment: 

        # Initialize a string
        text = ""

        # Add each character to create a line
        for character in line: 
            text += character

        # Print the line of the environment
        print(text)

    # Retstore value of current grid square
    environment[car_position[0]][car_position[1]] = temp

def clear():
    """
    This method clears the print output
    """    
    os.system( 'cls' )

def get_random_start_position(environment):
    """
    This method reads in the environment and selects a random
    starting position on the racetrack (y, x). Note that 
    (0,0) corresponds to the upper left corner of the racetrack.
    :param list environment: list of lines
    :return random starting coordinate (y,x) on the racetrack
    :rtype tuple
    """
    # Collect all possible starting positions on the racetrack
    starting_positions = []

    # For each row in the environment
    for y,row in enumerate(environment):

        # For each column in each row of the environment
        for x,col in enumerate(row):

            # If we are at the starting position
            if col == START:

                # Add the coordiante to the list of available
                # starting positions in the environment
                starting_positions += [(y,x)]

    # Random shuffle the list of starting positions
    shuffle(starting_positions)

    # Select a starting position
    return starting_positions[0]

def get_new_velocity(old_vel,accel,min_vel=MIN_VELOCITY,max_vel=MAX_VELOCITY):
    """
    Get the new velocity values
    :param tuple old_vel: (vy, vx)
    :param tuple accel: (ay, ax)
    :param int min_vel: Minimum velocity of the car
    :param int max_vel: Maximum velocity of the car
    :return new velocities in y and x directions
    """
    new_y = old_vel[0] + accel[0] 
    new_x = old_vel[1] + accel[1]
    if new_x < min_vel: new_x = min_vel
    if new_x > max_vel: new_x = max_vel
    if new_y < min_vel: new_y = min_vel
    if new_y > max_vel: new_y = max_vel
    
    # Return the new velocities
    return new_y, new_x

def get_new_position(old_loc, vel, environment):
    """
    Get a new position using the old position and the velocity
    :param tuple old_loc: (y,x) position of the car
    :param tuple vel: (vy,vx) velocity of the car
    :param list environment
    :return y+vy, x+vx: (new_y,new_x)
    """
    y,x = old_loc[0], old_loc[1]
    vy, vx = vel[0], vel[1]

    # new_y = y+vy, new_x = x + vx    
    return y+vy, x+vx

def get_nearest_open_cell(environment, y_crash, x_crash, vy = 0, vx = (
        0), open = [TRACK, START, GOAL]):
    """
    Locate the nearest open cell in order to handle crash scenario.
    Distance is calculated as the Manhattan distance.
    Start from the crash grid square and expand outward from there with
    a radius of 1, 2, 3, etc. Forms a diamond search pattern.
    
    For example, a Manhattan distance of 2 would look like the following:     
            .
           ...
          ..#..
           ... 
            .   
    If velocity is provided, search in opposite direction of velocity so that
    there is no movement over walls
    :param list environment
    :param int ycrash: y coordinate where crash happened
    :param int xcrash: x coordinate where crash happened
    :param int vy: velocity in y direction when crash occurred
    :param int vx: velocity in x direction when crash occurred
    :param list of strings open: Contains environment types
    :return tuple of the nearest open y and x position on the racetrack
    """ 
    # Record number of rows (lines) and columns in the environment
    rows = len(environment)
    cols = len(environment[0])    
   
    # Add expanded coverage for searching for nearest open cell
    max_radius = max(rows,cols)

    # Generate a search radius for each scenario
    for radius in range(max_radius):

        # If car is not moving in y direction
        if vy == 0: 
            y_off_range = range(-radius, radius + 1)
        # If the velocity in y-direction is negative
        elif vy < 0:
            # Search in the positive direction
            y_off_range = range(0, radius + 1)
        else:
            # Otherwise search in the negative direction
            y_off_range = range(-radius, 1)

        # For each value in the search radius range of y
        for y_offset in y_off_range:

            # Start near to crash site and work outwards from there
            y = y_crash + y_offset
            x_radius = radius - abs(y_offset)

            # If car is not moving in x direction
            if vx == 0:
                x_range = range(x_crash - x_radius, x_crash + x_radius + 1)
            # If the velocity in x-direction is negative
            elif vx < 0:
                x_range = range(x_crash, x_crash + x_radius + 1)
            # If the velocity in y-direction is positive
            else:
                x_range = range(x_crash - x_radius, x_crash + 1)

            # For each value in the search radius range of x
            for x in x_range:
                # We can't go outside the environment(racetrack) boundary
                if y < 0 or y >= rows: continue
                if x < 0 or x >= cols: continue

                # If we find and open cell, return that (y,x) open cell
                if environment[y][x] in open: 
                    return(y,x)        
    
    # No open grid squares found on the racetrack
    return

def act(old_y, old_x, old_vy, old_vx, accel, environment, deterministic=(
    False),bad_crash = False):
    """
    This method generates the new state s' (position and velocity) from the old
    state s and the action a taken by the race car. It also takes as parameters
    the two different crash scenarios (i.e. go to nearest
    open position on the race track or go back to start)
    :param int old_y: The old y position of the car
    :param int old_x: The old x position of the car
    :param int old_vy: The old y velocity of the car
    :param int old_vx: The old x velocity of the car
    :param tuple accel: (ay,ax) - acceleration in y and x directions
    :param list environment: The racetrack
    :param boolean deterministic: True if we always follow the policy
    :param boolean bad_crash: True if we return to start after crash
    :return s' where s' = new_y, new_x, new_vy, and new_vx
    :rtype int
    """ 
    # This method is deterministic if the same output is returned given
    # the same input information
    if not deterministic:

        # If action fails (car fails to take the prescribed action a)
        if random() > PROB_ACCELER_SUCCESS: 
            #print("Car failed to accelerate!")
            accel = (0,0)
 
    # Using the old velocity values and the new acceleration values,
    # get the new velocity value
    new_vy, new_vx = get_new_velocity((old_vy,old_vx), accel)

    # Using the new velocity values, update with the new position
    temp_y, temp_x = get_new_position((old_y,old_x), (new_vy, new_vx),( 
                                     environment))

    # Find the nearest open cell on the racetrack to this new position
    new_y, new_x = get_nearest_open_cell(environment, temp_y, temp_x, new_vy, 
                                     new_vx)
    # If a crash happens (i.e. new position is not equal to the nearest
    # open position on the racetrack
    if new_y != temp_y or new_x != temp_x:

        # If this is a crash in which we would have to return to the
        # starting position of the racetrack and we are not yet
        # on the finish line
        if bad_crash and environment[new_y][new_x] != GOAL:

            # Return to the start of the race track
            new_y, new_x = get_random_start_position(environment)
        
        # Velocity of the race car is set to 0.
        new_vy, new_vx = 0,0

    # Return the new state
    return new_y, new_x, new_vy, new_vx

def get_policy_from_Q(cols, rows, vel_range, Q, actions):
    """
    This method returns the policy pi(s) based on the action taken in each state
    that maximizes the value of Q in the table Q[s,a]. This is pi*(s)...the
    best action that the race car should take in each state is the one that 
    maximizes the value of Q. (* means optimal)
    :param int cols: Number of columns in the environment
    :param int rows: Number of rows (i.e. lines) in the environment
    :param list vel_range: Range of the velocity of the race car 
    :param list of tuples actions: actions = [(ay,ax),(ay,ax)....]
    :return pi : the policy
    :rtype: dictionary: key is the state tuple, value is the 
       action tuple (ay,ax)
    """
    # Create an empty dictionary called pi
    pi = {}

    # For each state s in the environment
    for y in range(rows): 
        for x in range(cols):
            for vy in vel_range:
                for vx in vel_range:
                    # Store the best action for each state...the one that
                    # maximizes the value of Q.
                    # argmax looks across all actions given a state and 
                    # returns the index ai of the maximum Q value
                    pi[(y,x,vy,vx)] = actions[np.argmax(Q[y][x][vy][vx])]        
                    
    # Return pi(s)
    return(pi)

def value_iteration(environment, bad_crash = False, reward = (
        0.0), no_training_iter = NO_TRAINING_ITERATIONS):
    """
    This method is the value iteration algorithm.
    :param list environment
    :param boolean bad_crash
    :param int reward of the terminal states (i.e. finish line)
    :param int no_training_iter
    :return policy pi(s) which maps a given state to an optimal action
    :rtype dictionary
    """
    # Calculate the number of rows and columns of the environment
    rows = len(environment)
    cols = len(environment[0])

    # Create a table V(s) that will store the optimal Q-value for each state. 
    # This table will help us determine when we should stop the algorithm and 
    # return the output. Initialize all the values of V(s) to arbitrary values, 
    # except the terminal state (i.e. finish line state) that has a value of 0.
    # values[y][x][vy][vx] 
    # Read from left to right, we create a list of vx values. Then for each
    # vy value we assign the list of vx values. Then for each x value, we assign
    # the list of vy values (which contain a list of vx values), etc.
    # This is called list comprehension.
    values = [[[[random() for _ in vel_range] for _ in vel_range] for _ in (
        line)] for line in environment]

    # Set the finish line states to 0
    for y in range(rows):
        for x in range(cols):
            # Terminal state has a value of 0
            if environment[y][x] == GOAL:
                for vy in vel_range:
                    for vx in vel_range:                 
                        values[y][x][vy][vx] = reward

    # Initialize all Q(s,a) to arbitrary values, except the terminal state 
    # (i.e. finish line states) that has a value of 0.
    # Q[y][x][vy][vx][ai]
    Q = [[[[[random() for _ in actions] for _ in vel_range] for _ in (
        vel_range)] for _ in line] for line in environment]

    # Set finish line state-action pairs to 0
    for y in range(rows):
        for x in range(cols):
            # Terminal state has a value of 0
            if environment[y][x] == GOAL:
                for vy in vel_range:
                    for vx in vel_range:   
                        for ai, a in enumerate(actions):                        
                            Q[y][x][vy][vx][ai] = reward

    # This is where we train the agent (i.e. race car). Training entails 
    # optimizing the values in the tables of V(s) and Q(s,a)
    for t in range(no_training_iter):

        # Keep track of the old V(s) values so we know if we reach stopping 
        # criterion
        values_prev = deepcopy(values)

        # When this value gets below the error threshold, we stop training.
        # This is the maximum change of V(s)
        delta = 0.0

        # For all the possible states s in S
        for y in range(rows):
            for x in range(cols):
                for vy in vel_range:
                    for vx in vel_range:
                        
                        # If the car crashes into a wall
                        if environment[y][x] == WALL:

                            # Wall states have a negative value
                            # I set some arbitrary negative value since
                            # we want to train the car not to hit walls
                            values[y][x][vy][vx] = -9.9

                            # Go back to the beginning
                            # of this inner for loop so that we set
                            # all the other wall states to a negative value
                            continue

                        # For each action a in the set of possible actions A
                        for ai, a in enumerate(actions):

                            # The reward is -1 for every state except
                            # for the finish line states
                            if environment[y][x] == GOAL:
                                r = reward
                            else:
                                r = -1

                            # Get the new state s'. s' is based on the current 
                            # state s and the current action a
                            new_y, new_x, new_vy, new_vx = act(
                                y,x,vy,vx,a,environment,deterministic = True, 
                                bad_crash = bad_crash)

                            # V(s'): value of the new state when taking action
                            # a from state s. This is the one step look ahead.
                            value_of_new_state = values_prev[new_y][new_x][
                                new_vy][new_vx]

                            # Get the new state s'. s' is based on the current 
                            # state s and the action (0,0)
                            new_y, new_x, new_vy, new_vx = act(
                                y,x,vy,vx,(0,0),environment,deterministic = (
                                    True), bad_crash = bad_crash)

                            # V(s'): value of the new state when taking action
                            # (0,0) from state s. This is the value if for some
                            # reason the race car attemps to accelerate but 
                            # fails
                            value_of_new_state_if_action_fails = values_prev[
                                new_y][new_x][new_vy][new_vx]

                            # Expected value of the new state s'
                            # Note that each state-action pair has a unique 
                            # value for s'
                            expected_value = (
                                PROB_ACCELER_SUCCESS * value_of_new_state) + (
                                PROB_ACCELER_FAILURE * (
                                    value_of_new_state_if_action_fails))

                            # Update the Q-value in Q[s,a]
                            # immediate reward + discounted future value
                            Q[y][x][vy][vx][ai] = r + (
                                DISC_RATE * expected_value)

                        # Get the action with the highest Q value
                        argMaxQ = np.argmax(Q[y][x][vy][vx])

                        # Update V(s)
                        values[y][x][vy][vx] = Q[y][x][vy][vx][argMaxQ]

        # Make sure all the rewards to 0 in the terminal state
        for y in range(rows):
            for x in range(cols):
                # Terminal state has a value of 0
                if environment[y][x] == GOAL:
                    for vy in vel_range:
                        for vx in vel_range:                 
                            values[y][x][vy][vx] = reward

        # See if the V(s) values are stabilizing
        # Finds the maximum change of any of the states. Delta is a float.
        delta = max([max([max([max([abs(values[y][x][vy][vx] - values_prev[y][
            x][vy][vx]) for vx in vel_range]) for vy in (
            vel_range)]) for x in range(cols)]) for y in range(rows)])

        # If the values of each state are stabilizing, return the policy
        # and exit this method.
        if delta < ERROR_THRES:
            return(get_policy_from_Q(cols, rows, vel_range, Q, actions))

    return(get_policy_from_Q(cols, rows, vel_range, Q, actions))

def do_time_trial(environment, policy, bad_crash = False, animate = True, 
                  max_steps = MAX_STEPS):
    """
    Race car will do a time trial on the race track according to the policy.   
    :param list environment
    :param dictionary policy: A dictionary containing the best action for a 
        given state. The key is the state y,x,vy,vx and value is the action 
        (ax,ay) acceleration
    :param boolean bad_crash: The crash scenario. If true, race car returns to
        starting position after crashes
    :param boolean animate: If true, show the car on the racetrack at each 
        timestep
    :return i: Total steps to complete race (i.e. from starting position to 
        finish line)
    :rtype int

    """
    # Copy the environment
    environment_display = deepcopy(environment)

    # Get a starting position on the race track
    starting_pos = get_random_start_position(environment)
    y,x = starting_pos
    vy,vx = 0,0  # We initialize velocity to 0

    # Keep track if we get stuck
    stop_clock = 0    

    # Begin time trial
    for i in range(max_steps):        

        # Show the race car on the racetrack
        if animate: 
            print_environment(environment_display, car_position = [y,x])
        
        # Get the best action given the current state
        a = policy[(y,x,vy,vx)]

        # If we are at the finish line, stop the time trial
        if environment[y][x] == GOAL: 
            return i 
        
        # Take action and get new a new state s'
        y,x,vy,vx = act(y, x, vy, vx, a, environment, bad_crash = bad_crash)

        # Determine if the car gets stuck
        if vy == 0 and vx == 0:
            stop_clock += 1
        else:
            stop_clock = 0

        # We have gotten stuck as the car has not been moving for 5 timesteps
        if stop_clock == 5:
            return max_steps
        
    # Program has timed out
    return max_steps

def main():
    """
    The main method of the program
    """    
    print("Welcome to the Racetrack Control Program!")
    print("Powered by the " + ALGORITHM_NAME + 
          " Reinforcement Learning Algorithm\n")
    print("Track: " + THIS_TRACK)
    print()
    print("What happens to the car if it crashes into a wall?")
    option_1 = """1. Starts from the nearest position on the track to the 
        place where it crashed."""
    option_2 = """2. Returns back to the original starting position."""
    print(option_1)
    print(option_2)
    crash_scenario = int(input("Crash scenario (1 or 2): "))
    no_training_iter = int(input(
        "Enter the initial number of training iterations (e.g. 5): "))
    print("\nThe race car is training. Please wait...")

    # Directory where the racetrack is located
    #racetrack_name = input("Enter the path to your input file: ") 
    racetrack_name = FILENAME
    racetrack = read_environment(racetrack_name)

    # How many times the race car will do a single time trial
    races = NO_RACES

    while(no_training_iter < MAX_TRAIN_ITER):
    
        # Keep track of the total number of steps
        total_steps = 0

        # Record the crash scenario
        bad_crash = False
        if crash_scenario == 1:
            bad_crash = False
        else:
            bad_crash = True

        # Retrieve the policy
        policy = value_iteration(racetrack, bad_crash = bad_crash,
                             no_training_iter=no_training_iter) 
 
        for each_race in range(races):
            total_steps += do_time_trial(racetrack, policy, bad_crash = (
            bad_crash), animate = True)

        print("Number of Training Iterations: " + str(no_training_iter))
        if crash_scenario == 1:
            print("Bad Crash Scenario: " + option_1)
        else:
            print("Bad Crash Scenario: " + option_2)
        print("Average Number of Steps the Race Car Needs to Take Before " + 
              "Finding the Finish Line: " + str(total_steps/races) + " steps\n")
        print("\nThe race car is training. Please wait...")

        # Delay 
        time.sleep(FRAME_TIME + 4)

        # Testing statistics
        test_stats_file = THIS_TRACK 
        test_stats_file += "_"
        test_stats_file += ALGORITHM_NAME + "_iter"
        test_stats_file += str(no_training_iter)+ "_cr" 
        test_stats_file += str(crash_scenario) + "_stats.txt" 

        ## Open a test_stats_file 
        outfile_ts = open(test_stats_file,"w")
        
        outfile_ts.write(
            "------------------------------------------------------------------\n")
        outfile_ts.write(ALGORITHM_NAME + " Summary Statistics\n")
        outfile_ts.write(
            "------------------------------------------------------------------\n")
        outfile_ts.write("Track: ") 
        outfile_ts.write(THIS_TRACK)
        outfile_ts.write("\nNumber of Training Iterations: " + str(no_training_iter))
        if crash_scenario == 1:
            outfile_ts.write("\nBad Crash Scenario: " + option_1 + "\n")
        else:
            outfile_ts.write("Bad Crash Scenario: " + option_2 + "\n")
        outfile_ts.write("Average Number of Steps the Race Car Took " + 
              "Before Finding the Finish Line: " + str(total_steps/races) + 
              " steps\n")

        # Show functioning of the program
        trace_runs_file = THIS_TRACK 
        trace_runs_file += "_"
        trace_runs_file += ALGORITHM_NAME + "_iter"
        trace_runs_file += str(no_training_iter) + "_cr"
        trace_runs_file += str(crash_scenario) + "_trace.txt"

        if no_training_iter <= 5:
            ## Open a new file to save trace runs
            outfile_tr = open(trace_runs_file,"w") 
        
            # Print trace runs that demonstrate proper functioning of the code
            outfile_tr.write(str(policy))  
            
            outfile_tr.close()

        ## Close the files        
        outfile_ts.close()

        no_training_iter += 5

main()

Q-Learning Code in Python

And here is the code for Q-Learning. Again, don’t be scared by how long this code is. I included a lot of comments so that you know what is going on at each step of the code (just copy and paste this into your favorite IDE!):

import os # Library enables the use of operating system dependent functionality
import time # Library handles time-related tasks
from random import shuffle # Import shuffle() method from the random module
from random import random # Import random() method from the random module
from copy import deepcopy # Enable deep copying
import numpy as np # Import Numpy library

# File name: q_learning.py
# Author: Addison Sears-Collins
# Date created: 8/14/2019
# Python version: 3.7
# Description: Implementation of the Q-learning reinforcement learning
# algorithm for the racetrack problem
# The racetrack problem is described in full detail in: 
# Barto, A. G., Bradtke, S. J., Singh, S. P. (1995). Learning to Act Using 
#   Real-time Dynamic Programming. Artificial Intelligence, 72(1-2):81–138.
# and 
# Sutton, Richard S., and Andrew G. Barto. Reinforcement learning : 
#   An Introduction. Cambridge, Massachusetts: The MIT Press, 2018. Print.
#   (modified version of Exercise 5.12 on pg. 111)

# Define constants
ALGORITHM_NAME = "Q_Learning"
FILENAME = "L-track.txt"
THIS_TRACK = "L_track"
START = 'S'
GOAL = 'F'
WALL = '#'
TRACK = '.'
MAX_VELOCITY = 5
MIN_VELOCITY = -5
DISC_RATE = 0.9  # Discount rate, also known as gamma. Determines by how much
                 # we discount the value of a future state s'
ERROR_THRES = 0.001 # Determine when Q-values stabilize (i.e.theta)
PROB_ACCELER_FAILURE = 0.20 # Probability car will try to take action a 
                            # according to policy pi(s) = a and fail.
PROB_ACCELER_SUCCESS = 1 - PROB_ACCELER_FAILURE
NO_TRAINING_ITERATIONS = 500000 # A single training iteration runs through all
                            # possible states s
TRAIN_ITER_LENGTH = 10 # The maximum length of each training iteration
MAX_TRAIN_ITER = 10000000 # Maximum number of training iterations
NO_RACES = 10 # How many times the race car does a single time trial from 
              # starting position to the finish line
LEARNING_RATE = 0.25 # If applicable, also known as alpha
MAX_STEPS = 500 # Maximum number of steps the car can take during time trial
FRAME_TIME = 0.1 # How many seconds between frames printed to the console

# Range of the velocity of the race car in both y and x directions
vel_range = range(MIN_VELOCITY, MAX_VELOCITY + 1)

# Actions the race car can take
# (acceleration in y direction, acceleration in x direction)
actions = [(-1,-1), (0,-1), (1,-1),
           (-1,0) , (0,0),  (1,0),
           (-1,1) , (0,1),  (1,1)]

def read_environment(filename):
    """
    This method reads in the environment (i.e. racetrack)
    :param str filename
    :return environment: list of lists
    :rtype list
    """
    # Open the file named filename in READ mode.
    # Make the file an object named 'file'
    with open(filename, 'r') as file:

        # Read until end of file using readline() 
        # readline() then returns a list of the lines
        # of the input file
        environment_data = file.readlines()
    
    # Close the file
    file.close()

    # Initialize an empty list
    environment = []

    # Adds a counter to each line in the environment_data list,
    # i is the index of each line and line is the actual contents.
    # enumerate() helps get not only the line of the environment but also 
    # the index of that line (i.e. row)
    for i,line in enumerate(environment_data):
        # Ignore the first line that contains the dimensions of the racetrack
        if i > 0:
            # Remove leading or trailing whitespace if applicable
            line = line.strip()

            # If the line is empty, ignore it
            if line == "": continue

            # Creates a list of lines. Within each line is a list of 
            # individual characters
            # The stuff inside append(stuff) first creates a new_list = []
            # It then appends all the values in a given line to that new 
            # list (e.g. new_list.append(all values inside the line))
            # Then we append that new list to the environment list.
            # Therefoer, environment is a list of lists.
            environment.append([x for x in line])

    # Return the environment (i.e. a list of lists/lines)
    return environment

def print_environment(environment, car_position = [0,0]):
    """
    This method reads in the environment and current 
    (y,x) position of the car and prints the environment to the console
    :param list environment
    :param list car_position 
    """
    # Store value of current grid square
    temp = environment[car_position[0]][car_position[1]]

    # Move the car to current grid square
    environment[car_position[0]][car_position[1]] = "X"

    # Delay 
    time.sleep(FRAME_TIME)

    # Clear the printed output
    clear()

    # For each line in the environment
    for line in environment: 

        # Initialize a string
        text = ""

        # Add each character to create a line
        for character in line: 
            text += character

        # Print the line of the environment
        print(text)

    # Retstore value of current grid square
    environment[car_position[0]][car_position[1]] = temp

def clear():
    """
    This method clears the print output
    """    
    os.system( 'cls' )

def get_random_start_position(environment):
    """
    This method reads in the environment and selects a random
    starting position on the racetrack (y, x). Note that 
    (0,0) corresponds to the upper left corner of the racetrack.
    :param list environment: list of lines
    :return random starting coordinate (y,x) on the racetrack
    :rtype tuple
    """
    # Collect all possible starting positions on the racetrack
    starting_positions = []

    # For each row in the environment
    for y,row in enumerate(environment):

        # For each column in each row of the environment
        for x,col in enumerate(row):

            # If we are at the starting position
            if col == START:

                # Add the coordiante to the list of available
                # starting positions in the environment
                starting_positions += [(y,x)]

    # Random shuffle the list of starting positions
    shuffle(starting_positions)

    # Select a starting position
    return starting_positions[0]

def act(old_y, old_x, old_vy, old_vx, accel, environment, deterministic=(
    False),bad_crash = False):
    """
    This method generates the new state s' (position and velocity) from the old
    state s and the action a taken by the race car. It also takes as parameters
    the two different crash scenarios (i.e. go to nearest
    open position on the race track or go back to start)
    :param int old_y: The old y position of the car
    :param int old_x: The old x position of the car
    :param int old_vy: The old y velocity of the car
    :param int old_vx: The old x velocity of the car
    :param tuple accel: (ay,ax) - acceleration in y and x directions
    :param list environment: The racetrack
    :param boolean deterministic: True if we always follow the policy
    :param boolean bad_crash: True if we return to start after crash
    :return s' where s' = new_y, new_x, new_vy, and new_vx
    :rtype int
    """ 
    # This method is deterministic if the same output is returned given
    # the same input information
    if not deterministic:

        # If action fails (car fails to take the prescribed action a)
        if random() > PROB_ACCELER_SUCCESS: 
            #print("Car failed to accelerate!")
            accel = (0,0)
 
    # Using the old velocity values and the new acceleration values,
    # get the new velocity value
    new_vy, new_vx = get_new_velocity((old_vy,old_vx), accel)

    # Using the new velocity values, update with the new position
    temp_y, temp_x = get_new_position((old_y,old_x), (new_vy, new_vx),( 
                                     environment))

    # Find the nearest open cell on the racetrack to this new position
    new_y, new_x = get_nearest_open_cell(environment, temp_y, temp_x, new_vy, 
                                     new_vx)
    # If a crash happens (i.e. new position is not equal to the nearest
    # open position on the racetrack
    if new_y != temp_y or new_x != temp_x:

        # If this is a crash in which we would have to return to the
        # starting position of the racetrack and we are not yet
        # on the finish line
        if bad_crash and environment[new_y][new_x] != GOAL:

            # Return to the start of the race track
            new_y, new_x = get_random_start_position(environment)
        
        # Velocity of the race car is set to 0.
        new_vy, new_vx = 0,0

    # Return the new state
    return new_y, new_x, new_vy, new_vx

def get_new_position(old_loc, vel, environment):
    """
    Get a new position using the old position and the velocity
    :param tuple old_loc: (y,x) position of the car
    :param tuple vel: (vy,vx) velocity of the car
    :param list environment
    :return y+vy, x+vx: (new_y,new_x)
    """
    y,x = old_loc[0], old_loc[1]
    vy, vx = vel[0], vel[1]

    # new_y = y+vy, new_x = x + vx    
    return y+vy, x+vx

def get_new_velocity(old_vel,accel,min_vel=MIN_VELOCITY,max_vel=MAX_VELOCITY):
    """
    Get the new velocity values
    :param tuple old_vel: (vy, vx)
    :param tuple accel: (ay, ax)
    :param int min_vel: Minimum velocity of the car
    :param int max_vel: Maximum velocity of the car
    :return new velocities in y and x directions
    """
    new_y = old_vel[0] + accel[0] 
    new_x = old_vel[1] + accel[1]
    if new_x < min_vel: new_x = min_vel
    if new_x > max_vel: new_x = max_vel
    if new_y < min_vel: new_y = min_vel
    if new_y > max_vel: new_y = max_vel
    
    # Return the new velocities
    return new_y, new_x

def get_nearest_open_cell(environment, y_crash, x_crash, vy = 0, vx = (
        0), open = [TRACK, START, GOAL]):
    """
    Locate the nearest open cell in order to handle crash scenario.
    Distance is calculated as the Manhattan distance.
    Start from the crash grid square and expand outward from there with
    a radius of 1, 2, 3, etc. Forms a diamond search pattern.
    
    For example, a Manhattan distance of 2 would look like the following:     
            .
           ...
          ..#..
           ... 
            .   
    If velocity is provided, search in opposite direction of velocity so that
    there is no movement over walls
    :param list environment
    :param int ycrash: y coordinate where crash happened
    :param int xcrash: x coordinate where crash happened
    :param int vy: velocity in y direction when crash occurred
    :param int vx: velocity in x direction when crash occurred
    :param list of strings open: Contains environment types
    :return tuple of the nearest open y and x position on the racetrack
    """ 
    # Record number of rows (lines) and columns in the environment
    rows = len(environment)
    cols = len(environment[0])    
   
    # Add expanded coverage for searching for nearest open cell
    max_radius = max(rows,cols)

    # Generate a search radius for each scenario
    for radius in range(max_radius):

        # If car is not moving in y direction
        if vy == 0: 
            y_off_range = range(-radius, radius + 1)
        # If the velocity in y-direction is negative
        elif vy < 0:
            # Search in the positive direction
            y_off_range = range(0, radius + 1)
        else:
            # Otherwise search in the negative direction
            y_off_range = range(-radius, 1)

        # For each value in the search radius range of y
        for y_offset in y_off_range:

            # Start near to crash site and work outwards from there
            y = y_crash + y_offset
            x_radius = radius - abs(y_offset)

            # If car is not moving in x direction
            if vx == 0:
                x_range = range(x_crash - x_radius, x_crash + x_radius + 1)
            # If the velocity in x-direction is negative
            elif vx < 0:
                x_range = range(x_crash, x_crash + x_radius + 1)
            # If the velocity in y-direction is positive
            else:
                x_range = range(x_crash - x_radius, x_crash + 1)

            # For each value in the search radius range of x
            for x in x_range:
                # We can't go outside the environment(racetrack) boundary
                if y < 0 or y >= rows: continue
                if x < 0 or x >= cols: continue

                # If we find and open cell, return that (y,x) open cell
                if environment[y][x] in open: 
                    return(y,x)        
    
    # No open grid squares found on the racetrack
    return

def get_policy_from_Q(cols, rows, vel_range, Q, actions):
    """
    This method returns the policy pi(s) based on the action taken in each state
    that maximizes the value of Q in the table Q[s,a]. This is pi*(s)...the
    best action that the race car should take in each state is the one that 
    maximizes the value of Q. (* means optimal)
    :param int cols: Number of columns in the environment
    :param int rows: Number of rows (i.e. lines) in the environment
    :param list vel_range: Range of the velocity of the race car 
    :param list of tuples actions: actions = [(ay,ax),(ay,ax)....]
    :return pi : the policy
    :rtype: dictionary: key is the state tuple, value is the 
       action tuple (ay,ax)
    """
    # Create an empty dictionary called pi
    pi = {}

    # For each state s in the environment
    for y in range(rows): 
        for x in range(cols):
            for vy in vel_range:
                for vx in vel_range:
                    # Store the best action for each state...the one that
                    # maximizes the value of Q.
                    # argmax looks across all actions given a state and 
                    # returns the index ai of the maximum Q value
                    pi[(y,x,vy,vx)] = actions[np.argmax(Q[y][x][vy][vx])]        
                    
    # Return pi(s)
    return(pi)

def q_learning(environment, bad_crash = False, reward = 0.0, no_training_iter =( 
    NO_TRAINING_ITERATIONS), train_iter_length = TRAIN_ITER_LENGTH):
    """ 
    Return a policy pi that maps states to actions
    Each episode uses a different initial state. This forces the agent to fully
    explore the environment to create a more informed Q[s,a] table.
    :param list environment
    :param boolean bad_crash
    :param int reward of the terminal states (i.e. finish line)
    :param int no_training_iter
    :param int train_iter_length
    :return policy pi(s) which maps a given state to an optimal action
    :rtype dictionary
    """
    rows = len(environment)
    cols = len(environment[0])    

    # Initialize all Q(s,a) to arbitrary values, except the terminal state 
    # (i.e. finish line states) that has a value of 0.
    # Q[y][x][vy][vx][ai]
    Q = [[[[[random() for _ in actions] for _ in vel_range] for _ in (
        vel_range)] for _ in line] for line in environment]

    # Set finish line state-action pairs to 0
    for y in range(rows):
        for x in range(cols):
            # Terminal state has a value of 0
            if environment[y][x] == GOAL:
                for vy in vel_range:
                    for vx in vel_range:   
                        for ai, a in enumerate(actions):                        
                            Q[y][x][vy][vx][ai] = reward

    # We run many training iterations for different initial states in order
    # to explore the environment as much as possible
    for iter in range(no_training_iter):
               
        # Reset all the terminal states to the value of the goal
        for y in range(rows):
            for x in range(cols): 
                if environment[y][x] == GOAL: 
                    Q[y][x] = [[[reward for _ in actions] for _ in (
                        vel_range)] for _ in vel_range] 
        
        # Select a random initial state
        # from anywhere on the racetrack
        y = np.random.choice(range(rows))
        x = np.random.choice(range(cols))
        vy = np.random.choice(vel_range) 
        vx = np.random.choice(vel_range) 

        # Do a certain number of iterations for each episode
        for t in range(train_iter_length):
            if environment[y][x] == GOAL: 
                break
            if environment[y][x] == WALL: 
                break

            # Choose the best action for the state s
            a = np.argmax(Q[y][x][vy][vx])           
            
            # Act and then observe a new state s'
            new_y, new_x, new_vy, new_vx = act(y, x, vy, vx, actions[
                a], environment, bad_crash = bad_crash) 
            r = -1

            # Update the Q table based on the immediate reward received from
            # taking action a in state s plus the discounted future reward
            Q[y][x][vy][vx][a] = ((1 - LEARNING_RATE)*Q[y][x][vy][vx][a] + 
                LEARNING_RATE*(r + DISC_RATE*max(Q[new_y][new_x][
                    new_vy][new_vx])))

            # The new state s' now becomes s
            y, x, vy, vx = new_y, new_x, new_vy, new_vx

    return(get_policy_from_Q(cols, rows, vel_range, Q, actions))


def do_time_trial(environment, policy, bad_crash = False, animate = True, 
                  max_steps = MAX_STEPS):
    """
    Race car will do a time trial on the race track according to the policy.   
    :param list environment
    :param dictionary policy: A dictionary containing the best action for a 
        given state. The key is the state y,x,vy,vx and value is the action 
        (ax,ay) acceleration
    :param boolean bad_crash: The crash scenario. If true, race car returns to
        starting position after crashes
    :param boolean animate: If true, show the car on the racetrack at each 
        timestep
    :return i: Total steps to complete race (i.e. from starting position to 
        finish line)
    :rtype int

    """
    # Copy the environment
    environment_display = deepcopy(environment)

    # Get a starting position on the race track
    starting_pos = get_random_start_position(environment)
    y,x = starting_pos
    vy,vx = 0,0  # We initialize velocity to 0

    # Keep track if we get stuck
    stop_clock = 0    

    # Begin time trial
    for i in range(max_steps):        

        # Show the race car on the racetrack
        if animate: 
            print_environment(environment_display, car_position = [y,x])
        
        # Get the best action given the current state
        a = policy[(y,x,vy,vx)]

        # If we are at the finish line, stop the time trial
        if environment[y][x] == GOAL: 
            return i 
        
        # Take action and get new a new state s'
        y,x,vy,vx = act(y, x, vy, vx, a, environment, bad_crash = bad_crash)

        # Determine if the car gets stuck
        if vy == 0 and vx == 0:
            stop_clock += 1
        else:
            stop_clock = 0

        # We have gotten stuck as the car has not been moving for 5 timesteps
        if stop_clock == 5:
            return max_steps
        
    # Program has timed out
    return max_steps

def main():
    """
    The main method of the program
    """    
    print("Welcome to the Racetrack Control Program!")
    print("Powered by the " + ALGORITHM_NAME + 
          " Reinforcement Learning Algorithm\n")
    print("Track: " + THIS_TRACK)
    print()
    print("What happens to the car if it crashes into a wall?")
    option_1 = """1. Starts from the nearest position on the track to the 
        place where it crashed."""
    option_2 = """2. Returns back to the original starting position."""
    print(option_1)
    print(option_2)
    crash_scenario = int(input("Crash scenario (1 or 2): "))
    no_training_iter = int(input(
        "Enter the initial number of training iterations (e.g. 500000): "))
    print("\nThe race car is training. Please wait...")

    # Directory where the racetrack is located
    #racetrack_name = input("Enter the path to your input file: ") 
    racetrack_name = FILENAME
    racetrack = read_environment(racetrack_name)

    # How many times the race car will do a single time trial
    races = NO_RACES

    while(no_training_iter <= MAX_TRAIN_ITER):
    
        # Keep track of the total number of steps
        total_steps = 0

        # Record the crash scenario
        bad_crash = False
        if crash_scenario == 1:
            bad_crash = False
        else:
            bad_crash = True

        # Retrieve the policy
        policy =  q_learning(racetrack, bad_crash = (
            bad_crash),no_training_iter=no_training_iter)
 
        for each_race in range(races):
            total_steps += do_time_trial(racetrack, policy, bad_crash = (
            bad_crash), animate = False)

        print("Number of Training Iterations: " + str(no_training_iter))
        if crash_scenario == 1:
            print("Bad Crash Scenario: " + option_1)
        else:
            print("Bad Crash Scenario: " + option_2)
        print("Average Number of Steps the Race Car Needs to Take Before " + 
              "Finding the Finish Line: " + str(total_steps/races) + " steps\n")
        print("\nThe race car is training. Please wait...")

        # Delay 
        time.sleep(FRAME_TIME + 4)

        # Testing statistics
        test_stats_file = THIS_TRACK 
        test_stats_file += "_"
        test_stats_file += ALGORITHM_NAME + "_iter"
        test_stats_file += str(no_training_iter)+ "_cr" 
        test_stats_file += str(crash_scenario) + "_stats.txt" 

        ## Open a test_stats_file 
        outfile_ts = open(test_stats_file,"w")
        
        outfile_ts.write(
            "------------------------------------------------------------------\n")
        outfile_ts.write(ALGORITHM_NAME + " Summary Statistics\n")
        outfile_ts.write(
            "------------------------------------------------------------------\n")
        outfile_ts.write("Track: ") 
        outfile_ts.write(THIS_TRACK)
        outfile_ts.write("\nNumber of Training Iterations: " + str(no_training_iter))
        if crash_scenario == 1:
            outfile_ts.write("\nBad Crash Scenario: " + option_1 + "\n")
        else:
            outfile_ts.write("Bad Crash Scenario: " + option_2 + "\n")
        outfile_ts.write("Average Number of Steps the Race Car Took " + 
              "Before Finding the Finish Line: " + str(total_steps/races) + 
              " steps\n")

        # Show functioning of the program
        trace_runs_file = THIS_TRACK 
        trace_runs_file += "_"
        trace_runs_file += ALGORITHM_NAME + "_iter"
        trace_runs_file += str(no_training_iter) + "_cr"
        trace_runs_file += str(crash_scenario) + "_trace.txt"

        if no_training_iter <= 5:
            ## Open a new file to save trace runs
            outfile_tr = open(trace_runs_file,"w") 
        
            # Print trace runs that demonstrate proper functioning of the code
            outfile_tr.write(str(policy))  
            
            outfile_tr.close()

        ## Close the files        
        outfile_ts.close()

        if no_training_iter == 500000:
            no_training_iter += 500000
        else:
            no_training_iter += 1000000
           
main()

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Experimental Output and Analysis

Here are the results:

value-iteration-1
value-iteration-2
q-learning-1
q-learning-2
q-learning-3

Analysis

Hypothesis 1: Both Algorithms Will Enable the Car to Finish the Race

Both the value iteration and Q-learning algorithms were successfully able to finish the race for both crash scenarios and for both the R-track and the L-track. The race car completed the R-track in fewer time steps than the L-track, which was expected.

The crash policy in which the car had to return to the starting position after it crashed versus going to the nearest open position negatively impacted performance for both algorithms. Time trial performance was superior for the value iteration algorithm compared to the Q learning algorithm. This result was expected given that the value iteration algorithm had access to the transition and the reward probabilities during the training phase. In other words, value iteration it gets a complete model of the entire track, whereas Q-learning has to be forced to explore the environment in order to learn.

Hypothesis 2: Value Iteration Will Learn Faster Than Q-Learning

My hypothesis was correct. Value iteration generated a learning policy faster than Q-learning because it had access to the transition and reward functions. Q-learning required more than 6,000,000 training iterations on the R-track to achieve the time trial performance that the value iteration algorithm was able to produce in only 45 training iterations (holding all other hyperparameters constant). And whereas the Q-learning algorithm took 2-3 hours to train to get good time trial results, value iteration never took more than 10 minutes for both the R-track and L-track under both of the bad crash scenarios.

Hypothesis 3: Bad Crash Version 1 Will Outperform Bad Crash Version 2

The results show that my hypothesis was correct. It took longer for the car to finish the race for the crash scenario in which the race car needed to return to the original starting position each time it crashed into a wall. In other words, Bad Crash Version 1 (return to start) performance was better than Bad Crash Version 2 (return to nearest open position) performance. These results are what I expected since always returning to the starting position after a crash hampers the ability of the race car to continually explore new states.

Summary and Conclusions

My hypotheses were correct. Here are the following conclusions:

  • Value iteration and Q-learning are powerful reinforcement learning algorithms that can enable an agent to learn autonomously.
  • Value iteration led to faster learning than the Q-learning algorithm.
  • A crash policy in which the race car always returns to the starting position after a crash negatively impacts performance.

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Video Demonstration

Here is a video demonstration of the algorithms in action.

References

Alpaydin, E. (2014). Introduction to Machine Learning. Cambridge, Massachusetts: The MIT Press.

Barto, A. G., Bradtke, S. J., & Singh, S. P. (1995). Learning to Act Using Real-Time Dynamic Programming. Artificial Intelligence, 81-138.

Russell, S. J., Norvig, P., & Davis, E. (2010). Artificial intelligence : A Modern Approach. Upper Saddle River, NJ: Prentice Hall.

Sutton, R. S., & Barto, A. G. (2018). Reinforcement learning : An Introduction . Cambridge, Massachusetts: The MIT Press.

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Artificial Feedforward Neural Network With Backpropagation From Scratch

In this post, I will walk you through how to build an artificial feedforward neural network trained with backpropagation, step-by-step. We will not use any fancy machine learning libraries, only basic Python libraries like Pandas and Numpy.

Our end goal is to evaluate the performance of an artificial feedforward neural network trained with backpropagation and to compare the performance using no hidden layers, one hidden layer, and two hidden layers. Five different data sets from the UCI Machine Learning Repository are used to compare performance: Breast Cancer, Glass, Iris, Soybean (small), and Vote.

We will use our neural network to do the following:

  • Predict if someone has breast cancer
  • Identify glass type
  • Identify flower species
  • Determine soybean disease type
  • Classify a representative as either a Democrat or Republican based on their voting patterns

I hypothesize that the neural networks with no hidden layers will outperform the networks with two hidden layers. My hypothesis is based on the notion that the simplest solutions are often the best solutions (i.e. Occam’s Razor).

The classification accuracy of the algorithms on the data sets will be evaluated as follows, using five-fold stratified cross-validation:

  • Accuracy = (number of correct predictions)/(total number of predictions)

Title image source: Wikimedia commons

Table of Contents

What is an Artificial Feedforward Neural Network Trained with Backpropagation?

neural_network-1

Background

An artificial feed-forward neural network (also known as multilayer perceptron) trained with backpropagation is an old machine learning technique that was developed in order to have machines that can mimic the brain. Neural networks were the focus of a lot of machine learning research during the 1980s and early 1990s but declined in popularity during the late 1990s.

Since 2010, neural networks have experienced a resurgence in popularity due to improvements in computing speed and the availability of massive amounts of data with which to train large-scale neural networks. In the real world, neural networks have been used to recognize speech, caption images, and even help self-driving cars learn how to park autonomously.

The Brain as Inspiration for Artificial Neural Networks

neuron_t_png

In order to understand neural networks, it helps to first take a look at the basic architecture of the human brain. The brain has 1011 neurons (Alpaydin, 2014). Neurons are cells inside the brain that process information.

Each neuron contains a number of input wires called dendrites. Each neuron also has one output wire called an axon. The axon is used to send messages to other neurons. The axon of a sending neuron is connected to the dendrites of the receiving neuron via a synapse.

So, in short, a neuron receives inputs from dendrites, performs a computation, and sends the output to other neurons via the axon. This process is how information flows through the brain. The messages sent between neurons are in the form of electric pulses.

An artificial neural network, the one used in machine learning, is a simplified model of the actual human neural network explained above. It is typically composed of zero or more layers.

neural-network

Each layer of the neural network is made up of nodes (analogous to neurons in the brain). Nodes of one layer are connected to nodes in another layer by connection weights, which are typically just floating-point numbers (e.g. 0.23342341). These numbers represent the strength of the connection between two nodes.

The job of a node in a hidden layer is to:

  1. Receive input values from each node in a preceding layer
  2. Compute a weighted sum of those input values
  3. Send that weighted sum through some activation function (e.g. logistic sigmoid function or hyperbolic tangent function)
  4. Send the result of the computation in #3 to each node in the next layer of the neural network.

Thus, the output from the nodes in a given layer becomes the input for all nodes in the next layer.

The output layer of a network does steps 1-3 above. However, the result of the computation from step #3 is a class prediction instead of an input to another layer (since the output layer is the final layer).

Here is a diagram of the process I explained above:

Here is a diagram showing a single layer neural network:

b stands for the bias term. This is a constant. It is like the b in the equation for a line, y = mx + b. It enables the model to have flexibility because, without that bias term, you cannot as easily adapt the weighted sum of inputs (i.e. mx) to fit the data (i.e. in the example of a simple line, the line cannot move up and down the y-axis without that b term).

w in the diagram above stands for the weights, and x stands for the input values.

Here is a similar diagram, but now it is a two-layer neural network instead of single layer.

And here is one last way to look at the same thing I explained above:

artificial_neuron_scheme

Note that the yellow circles on the left represent the input values. w represents the weights. The sigma inside the box means that we calculated the weighted sum of the input values. We run that through the activation function f(S)…e.g. sigmoid function. And then out of that, pops the output, which is passed on to the nodes in the following layer.

Neural networks that contain many layers, for example more than 100, are called deep neural networks. Deep neural networks are the cornerstone of the rapidly growing field known as deep learning.

Training Phase

The objective during the training phase of a neural network is to determine all the connection weights. At the start of training, the weights of the network are initialized to small random values close to 0. After this step, training proceeds to the two main phases of the algorithm: forward propagation and backpropagation.

Forward Propagation

During the forward propagation phase of a neural network, we process one instance (i.e. one set of inputs) at a time. Hidden layers extract important features contained in the input data by computing a weighted sum of the inputs and running the result through the logistic sigmoid activation function. This output relays to nodes in the next hidden layer where the data is transformed yet again. This process continues until the data reaches the output layer.

The output of the output layer is a predicted class value, which in this project is a one-hot encoded class prediction vector. The index of the vector corresponds to each class. For example, if a 1 is in the 0 index of the vector (and a 0 is in all other indices of the vector), the class prediction is class 0. Because we are dealing with 0s and 1s, the output vector can also be considered the probability that an instance is in a given class.

Backpropagation

After the input signal produced by a training instance propagates through the network one layer at a time to the output layer, the backpropagation phase commences. An error value is calculated at the output layer. This error corresponds to the difference between the class predicted by the network and the actual (i.e. true) class of the training instance.

The prediction error is then propagated backward from the output layer to the input layer. Blame for the error is assigned to each node in each layer, and then the weights of each node of the neural network are updated accordingly (with the goal to make more accurate class predictions for the next instance that flows through the neural network) using stochastic gradient descent for the weight optimization procedure.

Note that weights of the neural network are adjusted on a training instance by training instance basis. This online learning method is the preferred one for classification problems of large size (Ĭordanov & Jain, 2013).

The forward propagation and backpropagation phases continue for a certain number of epochs. A single epoch finishes when each training instance has been processed exactly once.

Testing Phase

Once the neural network has been trained, it can be used to make predictions on new, unseen test instances. Test instances flow through the network one-by-one, and the resulting output (which is a vector of class probabilities) determines the classification. 

Helpful Video

Below is a helpful video by Andrew Ng, a professor at Stanford University, that explains neural networks and is helpful for getting your head around the math. The video gets pretty complicated in some spots (esp. where he starts writing all sorts of mathematical notation and derivatives). My advice is to lookup anything that he explains that isn’t clear. Take it slow as you are learning about neural networks. There is no rush. This stuff isn’t easy to understand on your first encounter with it. Over time, the fog will begin to lift, and you will be able to understand how it all works.

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Artificial Feedforward Neural Network Trained with Backpropagation Algorithm Design

The Logistic Regression algorithm was implemented from scratch. The Breast Cancer, Glass, Iris, Soybean (small), and Vote data sets were preprocessed to meet the input requirements of the algorithms. I used five-fold stratified cross-validation to evaluate the performance of the models.

Required Data Set Format for Feedforward Neural Network Trained with Backpropagation

Columns (0 through N)

  • 0: Instance ID
  • 1: Attribute 1
  • 2: Attribute 2
  • 3: Attribute 3
  • N: Actual Class

The program then adds two additional columns for the testing set.

  • N + 1: Predicted Class
  • N + 2: Prediction Correct? (1 if yes, 0 if no)

Breast Cancer Data Set

This breast cancer data set contains 699 instances, 10 attributes, and a class – malignant or benign (Wolberg, 1992).

Modification of Attribute Values

  • The actual class value was changed to “Benign” or “Malignant.”
  • Attribute values were normalized to be in the range 0 to 1.
  • Class values were vectorized using one-hot encoding.

Missing Data

There were 16 missing attribute values, each denoted with a “?”. I chose a random number between 1 and 10 (inclusive) to fill in the data.

Glass Data Set

This glass data set contains 214 instances, 10 attributes, and 7 classes (German, 1987). The purpose of the data set is to identify the type of glass.

Modification of Attribute Values

  • Attribute values were normalized to be in the range 0 to 1.
  • Class values were vectorized using one-hot encoding.

Missing Data

There are no missing values in this data set.

Iris Data Set

This data set contains 3 classes of 50 instances each (150 instances in total), where each class refers to a different type of iris plant (Fisher, 1988).

Modification of Attribute Values

  • Attribute values were normalized to be in the range 0 to 1.
  • Class values were vectorized using one-hot encoding.

Missing Data

There were no missing attribute values.

Soybean Data Set (small)

This soybean (small) data set contains 47 instances, 35 attributes, and 4 classes (Michalski, 1980). The purpose of the data set is to determine the disease type.

Modification of Attribute Values

  • Attribute values were normalized to be in the range 0 to 1.
  • Class values were vectorized using one-hot encoding.
  • Attribute values that were all the same value were removed.

Missing Data

There are no missing values in this data set.

Vote Data Set

This data set includes votes for each of the U.S. House of Representatives Congressmen (435 instances) on the 16 key votes identified by the Congressional Quarterly Almanac (Schlimmer, 1987). The purpose of the data set is to identify the representative as either a Democrat or Republican.

  • 267 Democrats
  • 168 Republicans

Modification of Attribute Values

  • I did the following modifications:
    • Changed all “y” to 1 and all “n” to 0.
  • Class values were vectorized using one-hot encoding.

Missing Data

Missing values were denoted as “?”. To fill in those missing values, I chose random number, either 0 (“No”) or 1 (“Yes”).

Stochastic Gradient Descent

I used stochastic gradient descent for optimizing the weights.

In normal gradient descent, we need to calculate the partial derivative of the cost function with respect to each weight. For each partial derivative, we have to tally up the terms for each training instance to compute the partial derivative of the cost function with respect to that weight. What this means is that, if we have a lot of attributes and a large dataset, gradient descent is slow. For this reason, stochastic gradient descent was chosen since weights are updated after each training instance (as opposed to after all training instances).

Here is a good video that explains stochastic gradient descent.

Logistic (Sigmoid) Activation Function

The logistic (sigmoid) activation function was used for the nodes in the neural network.

Description of Any Tuning Process Applied

Learning Rate

Some tuning was performed in this project. The learning rate was set to 0.1, which was different than the 0.01 value that is often used for multi-layer feedforward neural networks (Montavon, 2012). Lower values resulted in much longer training times and did not result in large improvements in classification accuracy.

Epochs

The number of epochs chosen for the main runs of the algorithm on the data sets was chosen to be 1000. Other values were tested, but the number of epochs did not have a large impact on classification accuracy.

Number of Nodes per Hidden Layer

In order to tune the number of nodes per hidden layer, I used a constant learning rate and constant number of epochs. I then calculated the classification accuracy for each data set for a set number of nodes per hidden layer. I performed this process using networks with one hidden layer and networks with two hidden layers. The results of this tuning process are below.

tuning-artificial-neural-network

Note that the mean classification accuracy across all data sets when one hidden layer was used for the neural network reached a peak at eight nodes per hidden layer. This value of eight nodes per hidden layer was used for the actual runs on the data sets.

For two hidden layers, the peak mean classification accuracy was attained at five nodes per hidden layer. Thus, when the algorithm was run on the data sets for two hidden layers, I used five nodes per hidden layer for each data set to compare the classification accuracy across the data sets.

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Artificial Feedforward Neural Network Trained with Backpropagation Algorithm in Python, Coded From Scratch

Here are the preprocessed data sets:

Here is the full code for the neural network. This is all you need to run the program:

import pandas as pd # Import Pandas library 
import numpy as np # Import Numpy library
from random import shuffle # Import shuffle() method from the random module
from random import seed # Import seed() method from the random module
from random import random # Import random() method from the random module
from collections import Counter # Used for counting
from math import exp # Import exp() function from the math module

# File name: neural_network.py
# Author: Addison Sears-Collins
# Date created: 7/30/2019
# Python version: 3.7
# Description: An artificial feedforward neural network trained 
#   with backpropagation (also called multilayer perceptron)

# Required Data Set Format
# Columns (0 through N)
# 0: Attribute 0
# 1: Attribute 1 
# 2: Attribute 2
# 3: Attribute 3 
# ...
# N: Actual Class

# 2 additional columns are added for the test set.
# N + 1: Predicted Class
# N + 2: Prediction Correct?

ALGORITHM_NAME = "Feedforward Neural Network With Backpropagation"
SEPARATOR = ","  # Separator for the data set (e.g. "\t" for tab data)

def normalize(dataset):
    """
    Normalize the attribute values so that they are between 0 and 1, inclusive
    :param pandas_dataframe dataset: The original dataset as a Pandas dataframe
    :return: normalized_dataset
    :rtype: Pandas dataframe
    """
    # Generate a list of the column names 
    column_names = list(dataset) 

    # For every column except the actual class column
    for col in range(0, len(column_names) - 1):  
        temp = dataset[column_names[col]] # Go column by column
        minimum = temp.min() # Get the minimum of the column
        maximum = temp.max() # Get the maximum of the column

        # Normalized all values in the column so that they
        # are between 0 and 1.
        # x_norm = (x_i - min(x))/(max(x) - min(x))
        dataset[column_names[col]] = dataset[column_names[col]] - minimum
        dataset[column_names[col]] = dataset[column_names[col]] / (
            maximum - minimum)

    normalized_dataset = dataset

    return normalized_dataset

def get_five_stratified_folds(dataset):
    """
    Implementation of five-fold stratified cross-validation. Divide the data
    set into five random folds. Make sure that the proportion of each class 
    in each fold is roughly equal to its proportion in the entire data set.
    :param pandas_dataframe dataset: The original dataset as a Pandas dataframe
    :return: five_folds
    :rtype: list of folds where each fold is a list of instances(i.e. examples)
    """
    # Create five empty folds
    five_folds = list()
    fold0 = list()
    fold1 = list()
    fold2 = list()
    fold3 = list()
    fold4 = list()

    # Get the number of columns in the data set
    class_column = len(dataset[0]) - 1

    # Shuffle the data randomly
    shuffle(dataset)

    # Generate a list of the unique class values and their counts
    classes = list()  # Create an empty list named 'classes'

    # For each instance in the dataset, append the value of the class
    # to the end of the classes list
    for instance in dataset:
        classes.append(instance[class_column])

    # Create a list of the unique classes
    unique_classes = list(Counter(classes).keys())

    # For each unique class in the unique class list
    for uniqueclass in unique_classes:

        # Initialize the counter to 0
        counter = 0
        
        # Go through each instance of the data set and find instances that
        # are part of this unique class. Distribute them among one
        # of five folds
        for instance in dataset:

            # If we have a match
            if uniqueclass == instance[class_column]:

                # Allocate instance to fold0
                if counter == 0:

                    # Append this instance to the fold
                    fold0.append(instance)

                    # Increase the counter by 1
                    counter += 1

                # Allocate instance to fold1
                elif counter == 1:

                    # Append this instance to the fold
                    fold1.append(instance)

                    # Increase the counter by 1
                    counter += 1

                # Allocate instance to fold2
                elif counter == 2:

                    # Append this instance to the fold
                    fold2.append(instance)

                    # Increase the counter by 1
                    counter += 1

                # Allocate instance to fold3
                elif counter == 3:

                    # Append this instance to the fold
                    fold3.append(instance)

                    # Increase the counter by 1
                    counter += 1

                # Allocate instance to fold4
                else:

                    # Append this instance to the fold
                    fold4.append(instance)

                    # Reset the counter to 0
                    counter = 0

    # Shuffle the folds
    shuffle(fold0)
    shuffle(fold1)
    shuffle(fold2)
    shuffle(fold3)
    shuffle(fold4)

    # Add the five stratified folds to the list
    five_folds.append(fold0)
    five_folds.append(fold1)
    five_folds.append(fold2)
    five_folds.append(fold3)
    five_folds.append(fold4)

    return five_folds

def initialize_neural_net(
    no_inputs, no_hidden_layers, no_nodes_per_hidden_layer, no_outputs):
    """
    Generates a new neural network that is ready to be trained.
    Network (list of layers): 0+ hidden layers, and output layer
    Input Layer (list of attribute values): A row from the training set 
    Hidden Layer (list of dictionaries): A set of nodes (i.e. neurons)
    Output Layer (list of dictionaries): A set of nodes, one node per class
    Node (dictionary): Contains a set of weights, one weight for each input 
      to the layer containing that node + an additional weight for the bias.
      Each node is represented as a dictionary that stores key-value pairs
      Each key corresponds to a property of that node (e.g. weights).
      Weights will be initialized to small random values between 0 and 1.
    :param int no_inputs: Numper of inputs (i.e. attributes)
    :param int no_hidden_layers: Numper of hidden layers (0 or more)
    :param int no_nodes_per_hidden_layer: Numper of nodes per hidden layer
    :param int no_outputs: Numper of outputs (one output node per class)
    :return: network
    :rtype:list (i.e. list of layers: hidden layers, output layer)
    """

    # Create an empty list
    network = list()

    # Create the the hidden layers
    hidden_layer = list()
    hl_counter = 0

    # Create the output layer
    output_layer = list()

    # If this neural network contains hidden layers
    if no_hidden_layers > 0:

        # Build one hidden layer at a time
        for layer in range(no_hidden_layers):

            # Reset to an empty hidden layer
            hidden_layer = list()

            # If this is the first hidden layer
            if hl_counter == 0:

                # Build one node at a time
                for node in range(no_nodes_per_hidden_layer):

                    initial_weights = list()
                    
                    # Each node in the hidden layer has no_inputs + 1 weights, 
                    # initialized to a random number in the range [0.0, 1.0)
                    for i in range(no_inputs + 1):
                        initial_weights.append(random())

                    # Add the node to the first hidden layer
                    hidden_layer.append({'weights':initial_weights})

                # Finished building the first hidden layer
                hl_counter += 1

                # Add this first hidden layer to the front of the neural 
                # network
                network.append(hidden_layer)

            # If this is not the first hidden layer
            else:

                # Build one node at a time
                for node in range(no_nodes_per_hidden_layer):

                    initial_weights = list()
                    
                    # Each node in the hidden layer has 
                    # no_nodes_per_hidden_layer + 1 weights, initialized to 
                    # a random number in the range [0.0, 1.0)
                    for i in range(no_nodes_per_hidden_layer + 1):
                        initial_weights.append(random())

                    hidden_layer.append({'weights':initial_weights})

                # Add this newly built hidden layer to the neural network
                network.append(hidden_layer)

        # Build the output layer
        for outputnode in range(no_outputs):

            initial_weights = list()
                    
            # Each node in the output layer has no_nodes_per_hidden_layer 
            # + 1 weights, initialized to a random number in 
            # the range [0.0, 1.0)
            for i in range(no_nodes_per_hidden_layer + 1):
                initial_weights.append(random())

            # Add this output node to the output layer
            output_layer.append({'weights':initial_weights})

        # Add the output layer to the neural network
        network.append(output_layer)
    
    # A neural network has no hidden layers
    else:

        # Build the output layer
        for outputnode in range(no_outputs):
        
            initial_weights = list()
                    
            # Each node in the hidden layer has no_inputs + 1 weights, 
            # initialized to a random number in the range [0.0, 1.0)
            for i in range(no_inputs + 1):
                initial_weights.append(random())

            # Add this output node to the output layer
            output_layer.append({'weights':initial_weights})

        network.append(output_layer)

    # Finished building the initial neural network
    return network

def weighted_sum_of_inputs(weights, inputs):
    """
    Calculates the weighted sum of inputs plus the bias
    :param list weights: A list of weights. Each node has a list of weights.
    :param list inputs: A list of input values. These can be a single row
        of attribute values or the output from nodes from the previous layer
    :return: weighted_sum
    :rtype: float
    """
    # We assume that the last weight is the bias value
    # The bias value is a special weight that does not multiply with an input
    # value (or we could assume its corresponding input value is always 1)
    # The bias is similar to the intercept constant b in y = mx + b. It enables
    # a (e.g. sigmoid) curve to be shifted to create a better fit
    # to the data. Without the bias term b, the line always goes through the 
    # origin (0,0) and cannot adapt as well to the data.
    # In y = mx + b, we assume b * x_0 where x_0 = 1

    # Initiate the weighted sum with the bias term. Assume the last weight is
    # the bias term
    weighted_sum = weights[-1]

    for index in range(len(weights) - 1):
        weighted_sum += weights[index] * inputs[index]

    return weighted_sum

def sigmoid(weighted_sum_of_inputs_plus_bias):
    """
    Run the weighted sum of the inputs + bias through
    the sigmoid activation function.
    :param float weighted_sum_of_inputs_plus_bias: Node summation term
    :return: sigmoid(weighted_sum_of_inputs_plus_bias)
    """
    return 1.0 / (1.0 + exp(-weighted_sum_of_inputs_plus_bias))

def forward_propagate(network, instance):
    """
    Instances move forward through the neural network from one layer
    to the next layer. At each layer, the outputs are calculated for each 
    node. These outputs are the inputs for the nodes in the next layer.
    The last set of outputs is the output for the nodes in the output 
    layer.
    :param list network: List of layers: 0+ hidden layers, 1 output layer
    :param list instance (a single training/test instance from the data set)
    :return: outputs
    :rtype: list
    """
    inputs = instance

    # For each layer in the neural network
    for layer in network:

        # These will store the outputs for this layer
        new_inputs = list()

        # For each node in this layer
        for node in layer:

            # Calculate the weighted sum + bias term
            weighted_sum = weighted_sum_of_inputs(node['weights'], inputs)

            # Run the weighted sum through the activation function
            # and store the result in this node's dictionary.
            # Now the node's dictionary has two keys, weights and output.
            node['output'] = sigmoid(weighted_sum)

            # Used for debugging
            #print(node)

            # Add the output of the node to the new_inputs list
            new_inputs.append(node['output'])

        # Update the inputs list
        inputs = new_inputs

    # We have reached the output layer
    outputs = inputs

    return outputs

def sigmoid_derivative(output):
    """
    The derivative of the sigmoid activation function with respect 
    to the weighted summation term of the node.
    Formally (after a lot of calculus), this derivative is:
        derivative = sigmoid(weighted_sum_of_inputs_plus_bias) * 
        (1 - sigmoid(weighted_sum_of_inputs_plus_bias))
                   = node_ouput * (1 - node_output)
    This method is used during the backpropagation phase. 
    :param list output: Output of a node (generated during the forward
        propagation phase)
    :return: sigmoid_der
    :rtype: float
    """
    return output * (1.0 - output)

def back_propagate(network, actual):
    """
    In backpropagation, the error is computed between the predicted output by 
    the network and the actual output as determined by the data set. This error 
    propagates backwards from the output layer to the first hidden layer. The 
    weights in each layer are updated along the way in response to the error. 
    The goal is to reduce the prediction error for the next training instance 
    that forward propagates through the network.
    :param network list: The neural network
    :param actual list: A list of the actual output from the data set
    """
    # Iterate in reverse order (i.e. starts from the output layer)
    for i in reversed(range(len(network))):

        # Work one layer at a time
        layer = network[i]

        # Keep track of the errors for the nodes in this layer
        errors = list()

        # If this is a hidden layer
        if i != len(network) - 1:

            # For each node_j in this hidden layer
            for j in range(len(layer)):

                # Reset the error value
                error = 0.0

                # Calculate the weighted error. 
                # The error values come from the error (i.e. delta) calculated
                # at each node in the layer just to the "right" of this layer. 
                # This error is weighted by the weight connections between the 
                # node in this hidden layer and the nodes in the layer just 
                # to the "right" of this layer.
                for node in network[i + 1]:
                    error += (node['weights'][j] * node['delta'])

                # Add the weighted error for node_j to the
                # errors list
                errors.append(error)
        
        # If this is the output layer
        else:

            # For each node in the output layer
            for j in range(len(layer)):
                
                # Store this node (i.e. dictionary)
                node = layer[j]

                # Actual - Predicted = Error
                errors.append(actual[j] - node['output'])

        # Calculate the delta for each node_j in this layer
        for j in range(len(layer)):
            node = layer[j]

            # Add an item to the node's dictionary with the 
            # key as delta.
            node['delta'] = errors[j] * sigmoid_derivative(node['output'])

def update_weights(network, instance, learning_rate):
    """
    After the deltas (errors) have been calculated for each node in 
    each layer of the neural network, the weights can be updated.
    new_weight = old_weight + learning_rate * delta * input_value
    :param list network: List of layers: 0+ hidden layers, 1 output layer
    :param list instance: A single training/test instance from the data set
    :param float learning_rate: Controls step size in the stochastic gradient
        descent procedure.
    """
    # For each layer in the network
    for layer_index in range(len(network)):

        # Extract all the attribute values, excluding the class value
        inputs = instance[:-1]

        # If this is not the first hidden layer
        if layer_index != 0:

            # Go through each node in the previous layer and add extract the
            # output from that node. The output from the previous layer
            # is the input to this layer.
            inputs = [node['output'] for node in network[layer_index - 1]]

        # For each node in this layer
        for node in network[layer_index]:

            # Go through each input value
            for j in range(len(inputs)):
                
                # Update the weights
                node['weights'][j] += learning_rate * node['delta'] * inputs[j]
          
            # Updating the bias weight 
            node['weights'][-1] += learning_rate * node['delta']

def train_neural_net(
    network, training_set, learning_rate, no_epochs, no_outputs):
    """
    Train a neural network that has already been initialized.
    Training is done using stochastic gradient descent where the weights
    are updated one training instance at a time rather than after the
    entire training set (as is the case with gradient descent).
    :param list network: The neural network, which is a list of layers
    :param list training_set: A list of training instances (i.e. examples)
    :param float learning_rate: Controls step size of gradient descent
    :param int no_epochs: How many passes we will make through training set
    :param int no_outputs: The number of output nodes (equal to # of classes)
    """
    # Go through the entire training set a fixed number of times (i.e. epochs)
    for epoch in range(no_epochs):
   
        # Update the weights one instance at a time
        for instance in training_set:

            # Forward propagate the training instance through the network
            # and produce the output, which is a list.
            outputs = forward_propagate(network, instance)

            # Vectorize the output using one hot encoding. 
            # Create a list called actual_output that is the same length 
            # as the number of outputs. Put a 1 in the place of the actual 
            # class.
            actual_output = [0 for i in range(no_outputs)]
            actual_output[int(instance[-1])] = 1
            
            back_propagate(network, actual_output)
            update_weights(network, instance, learning_rate)

def predict_class(network, instance):
    """
    Make a class prediction given a trained neural network and
    an instance from the test data set.
    :param list network: The neural network, which is a list of layers
    :param list instance: A single training/test instance from the data set
    :return class_prediction
    :rtype int
    """
    outputs = forward_propagate(network, instance)

    # Return the index that has the highest probability. This index
    # is the class value. Assume class values begin at 0 and go
    # upwards by 1 (i.e. 0, 1, 2, ...)
    class_prediction = outputs.index(max(outputs))
    
    return class_prediction

def calculate_accuracy(actual, predicted):
    """
    Calculates the accuracy percentages
    :param list actual: Actual class values
    :param list predicted: predicted class values
    :return: classification_accuracy
    :rtype: float (as a percentage)
    """
    number_of_correct_predictions = 0
    for index in range(len(actual)):
        if actual[index] == predicted[index]:
            number_of_correct_predictions += 1
    
    classification_accuracy = (
        number_of_correct_predictions / float(len(actual))) * 100.0
    return classification_accuracy

def get_test_set_predictions(
    training_set, test_set, learning_rate, no_epochs, 
    no_hidden_layers, no_nodes_per_hidden_layer):
    """
    This method is the workhorse. 
    A new neutal network is initialized.
    The network is trained on the training set.
    The trained neural network is used to generate predictions on the
    test data set.
    :param list training_set
    :param list test_set
    :param float learning_rate
    :param int no_epochs
    :param int no_hidden_layers
    :param int no_nodes_per_hidden_layer
    :return network, class_predictions
    :rtype list, list
    """
    # Get the number of attribute values
    no_inputs = len(training_set[0]) - 1

    # Calculate the number of unique classes
    no_outputs = len(set([instance[-1] for instance in training_set]))
    
    # Build a new neural network
    network = initialize_neural_net(
        no_inputs, no_hidden_layers, no_nodes_per_hidden_layer, no_outputs)

    train_neural_net(
        network, training_set, learning_rate, no_epochs, no_outputs)
    
    # Store the class predictions for each test instance
    class_predictions = list()
    for instance in test_set:
        cl_prediction = predict_class(network, instance)
        class_predictions.append(cl_prediction)

    # Return the learned model as well as the class predictions
    return network, class_predictions

###############################################################

def main():
    """
    The main method of the program
    """
    LEARNING_RATE = 0.1 # Used for stochastic gradient descent procedure
    NO_EPOCHS = 1000 # Epoch is one complete pass through training data
    NO_HIDDEN_LAYERS = 1 # Number of hidden layers
    NO_NODES_PER_HIDDEN_LAYER = 8 # Number of nodes per hidden layer

    # Welcome message
    print("Welcome to the " +  ALGORITHM_NAME + " Program!")
    print()

    # Directory where data set is located
    #data_path = input("Enter the path to your input file: ") 
    data_path = "vote.txt"

    # Read the full text file and store records in a Pandas dataframe
    pd_data_set = pd.read_csv(data_path, sep=SEPARATOR)

    # Show functioning of the program
    #trace_runs_file = input("Enter the name of your trace runs file: ") 
    trace_runs_file = "vote_nn_trace_runs.txt"

    ## Open a new file to save trace runs
    outfile_tr = open(trace_runs_file,"w") 

    # Testing statistics
    #test_stats_file = input("Enter the name of your test statistics file: ") 
    test_stats_file = "vote_nn_test_stats.txt"

    ## Open a test_stats_file 
    outfile_ts = open(test_stats_file,"w")

    # Generate a list of the column names 
    column_names = list(pd_data_set) 

    # The input layer in the neural network 
    # will have one node for each attribute value
    no_of_inputs = len(column_names) - 1

    # Make a list of the unique classes
    list_of_unique_classes = pd.unique(pd_data_set["Actual Class"])

    # The output layer in the neural network 
    # will have one node for each class value
    no_of_outputs = len(list_of_unique_classes)

    # Replace all the class values with numbers, starting from 0
    # in the Pandas dataframe.
    for cl in range(0, len(list_of_unique_classes)):
        pd_data_set["Actual Class"].replace(
            list_of_unique_classes[cl], cl ,inplace=True)

    # Normalize the attribute values so that they are all between 0 
    # and 1, inclusive
    normalized_pd_data_set = normalize(pd_data_set)

    # Convert normalized Pandas dataframe into a list
    dataset_as_list = normalized_pd_data_set.values.tolist()

    # Set the seed for random number generator
    seed(1)

    # Get a list of 5 stratified folds because we are doing
    # five-fold stratified cross-validation
    fv_folds = get_five_stratified_folds(dataset_as_list)
    
    # Keep track of the scores for each of the five experiments
    scores = list()
    
    experiment_counter = 0
    for fold in fv_folds:
        
        print()
        print("Running Experiment " + str(experiment_counter) + " ...")
        print()
        outfile_tr.write("Running Experiment " + str(
            experiment_counter) + " ...\n")
        outfile_tr.write("\n")

        # Get all the folds and store them in the training set
        training_set = list(fv_folds)

        # Four folds make up the training set
        training_set.remove(fold)        

        # Combined all the folds so that all we have is a list
        # of training instances
        training_set = sum(training_set, [])
        
        # Initialize a test set
        test_set = list()
        
        # For each instance in this test fold
        for instance in fold:
            
            # Create a copy and store it
            copy_of_instance = list(instance)
            test_set.append(copy_of_instance)
        
        # Get the trained neural network and the predicted values
        # for each test instance
        neural_net, predicted_values = get_test_set_predictions(
            training_set, test_set,LEARNING_RATE,NO_EPOCHS,
            NO_HIDDEN_LAYERS,NO_NODES_PER_HIDDEN_LAYER)
        actual_values = [instance[-1] for instance in fold]
        accuracy = calculate_accuracy(actual_values, predicted_values)
        scores.append(accuracy)

        # Print the learned model
        print("Experiment " + str(
            experiment_counter) + " Trained Neural Network")
        print()
        for layer in neural_net:
            print(layer)
        print()
        outfile_tr.write("Experiment " + str(
            experiment_counter) + " Trained Neural Network")
        outfile_tr.write("\n")
        outfile_tr.write("\n")
        for layer in neural_net:
            outfile_tr.write(str(layer))
            outfile_tr.write("\n")
        outfile_tr.write("\n\n")

        # Print the classifications on the test instances
        print("Experiment " + str(
            experiment_counter) + " Classifications on Test Instances")
        print()
        outfile_tr.write("Experiment " + str(
            experiment_counter) + " Classifications on Test Instances")
        outfile_tr.write("\n\n")
        test_df = pd.DataFrame(test_set, columns=column_names)

        # Add 2 additional columns to the testing dataframe
        test_df = test_df.reindex(
        columns=[*test_df.columns.tolist(
        ), 'Predicted Class', 'Prediction Correct?'])

        # Add the predicted values to the "Predicted Class" column
        # Indicate if the prediction was correct or not.
        for pre_val_index in range(len(predicted_values)):
            test_df.loc[pre_val_index, "Predicted Class"] = predicted_values[
                pre_val_index]
            if test_df.loc[pre_val_index, "Actual Class"] == test_df.loc[
                pre_val_index, "Predicted Class"]:
                test_df.loc[pre_val_index, "Prediction Correct?"] = "Yes"
            else:
                test_df.loc[pre_val_index, "Prediction Correct?"] = "No"

        # Replace all the class values with the name of the class
        for cl in range(0, len(list_of_unique_classes)):
            test_df["Actual Class"].replace(
                cl, list_of_unique_classes[cl] ,inplace=True)
            test_df["Predicted Class"].replace(
                cl, list_of_unique_classes[cl] ,inplace=True)

        # Print out the test data frame
        print(test_df)   
        print()
        print()
        outfile_tr.write(str(test_df))   
        outfile_tr.write("\n\n")

        # Go to the next experiment
        experiment_counter += 1
    
    print("Experiments Completed.\n")
    outfile_tr.write("Experiments Completed.\n\n")

    # Print the test stats   
    print("------------------------------------------------------------------")
    print(ALGORITHM_NAME + " Summary Statistics")
    print("------------------------------------------------------------------")
    print("Data Set : " + data_path)
    print()
    print("Learning Rate: " + str(LEARNING_RATE))
    print("Number of Epochs: " + str(NO_EPOCHS))
    print("Number of Hidden Layers: " + str(NO_HIDDEN_LAYERS))
    print("Number of Nodes Per Hidden Layer: " + str(
        NO_NODES_PER_HIDDEN_LAYER))
    print()
    print("Accuracy Statistics for All 5 Experiments: %s" % scores)
    print()
    print()
    print("Classification Accuracy: %.3f%%" % (
        sum(scores)/float(len(scores))))

    outfile_ts.write(
        "------------------------------------------------------------------\n")
    outfile_ts.write(ALGORITHM_NAME + " Summary Statistics\n")
    outfile_ts.write(
        "------------------------------------------------------------------\n")
    outfile_ts.write("Data Set : " + data_path +"\n\n")
    outfile_ts.write("Learning Rate: " + str(LEARNING_RATE) + "\n")
    outfile_ts.write("Number of Epochs: " + str(NO_EPOCHS) + "\n")
    outfile_ts.write("Number of Hidden Layers: " + str(
        NO_HIDDEN_LAYERS) + "\n")
    outfile_ts.write("Number of Nodes Per Hidden Layer: " + str(
        NO_NODES_PER_HIDDEN_LAYER) + "\n")
    outfile_ts.write(
        "Accuracy Statistics for All 5 Experiments: %s" % str(scores))
    outfile_ts.write("\n\n")
    outfile_ts.write("Classification Accuracy: %.3f%%" % (
        sum(scores)/float(len(scores))))

    ## Close the files
    outfile_tr.close()
    outfile_ts.close()

main()

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Artificial Feedforward Neural Network Trained with Backpropagation Output

Here are the trace runs:

Here are the results:

full-results-neural-network

Here are the test statistics for each data set:

Analysis

Breast Cancer Data Set

The breast cancer data set results were in line with what I expected. The simpler model, the one with no hidden layers, ended up generating the highest classification accuracy. Classification accuracy was just short of 97%. In other words, the neural network that had no hidden layers successfully classified a patient as either malignant or benign with an almost 97% accuracy.

These results also suggest that the amount of training data has a direct impact on performance. Higher amounts of data (699 instances in this case) can lead to better learning and better classification accuracy on new, unseen instances.

Glass Data Set

The performance of the neural network on the glass data set was the worst out of all of the data sets. The ability of the network to correctly identify the type of glass given the attribute values never exceeded 70%.

I hypothesize that the poor performance on the glass data set is due to the high numbers of classes combined with a relatively smaller data set.

Iris Data Set

Classification accuracy was superb on the iris dataset, attaining a classification accuracy around 97%. The results of the iris dataset were surprising given that the more complicated neural network with two hidden layers and five nodes per hidden layer outperformed the simpler neural network that had no hidden layers. In this case, it appears that the iris dataset benefited from the increasing layers of abstraction provided by a higher number of layers.

Soybean Data Set (small)

Performance on the soybean data set was stellar and was the highest of all of the data sets but also had the largest standard deviation for the classification accuracy. Note that classification accuracy reached a peak of 100% using one hidden layer and eight nodes for the hidden layer. However, when I added an additional hidden layer, classification accuracy dropped to under 70%.

The reason for the high standard deviation of the classification accuracy is unclear, but I hypothesize it has to do with the relatively small number of training instances. Future work would need to be performed with the soybean large dataset available from the UCI Machine Learning Repository to see if these results remain consistent.

The results of the soybean runs suggest that large numbers of relevant attributes can help a machine learning algorithm create more accurate classifications.

Vote Data Set

The vote data set did not yield the stellar performance of the soybean data set, but classification accuracy was still solid at ~96% using one hidden layer and eight nodes per hidden layer. These results are in line with what I expected because voting behavior should provide a powerful predictor of whether a candidate is a Democrat or Republican. I would have been surprised had I observed classification accuracies that were lower since members of Congress tend to vote along party lines on most issues.

Summary and Conclusions

My hypothesis was incorrect. In some cases, simple neural networks with no hidden layers outperformed more complex neural networks with 1+ hidden layers. However, in other cases, more complex neural networks with multiple hidden layers outperformed the network with no hidden layers. The reason why some data is more amenable to networks with hidden layers instead of without hidden layers is unclear.

Other conclusions include the following:

  • Higher amounts of data can lead to better learning and better classification accuracy on new, unseen instances.
  • Large numbers of relevant attributes can help a neural network create more accurate classifications.
  • Neural networks are powerful and can achieve excellent results on both binary and multi-class classification problems.

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References

Alpaydin, E. (2014). Introduction to Machine Learning. Cambridge, Massachusetts: The MIT Press.

Fisher, R. (1988, July 01). Iris Data Set. Retrieved from Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/iris

German, B. (1987, September 1). Glass Identification Data Set. Retrieved from UCI Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Glass+Identification

Ĭordanov, I., & Jain, L. C. (2013). Innovations in Intelligent Machines –3 : Contemporary Achievements in Intelligent Systems. Berlin: Springer.

Michalski, R. (1980). Learning by being told and learning from examples: an experimental comparison of the two methodes of knowledge acquisition in the context of developing an expert system for soybean disease diagnosis. International Journal of Policy Analysis and Information Systems, 4(2), 125-161.

Montavon, G. O. (2012). Neural Networks : Tricks of the Trade. New York: Springer.

Schlimmer, J. (1987, 04 27). Congressional Voting Records Data Set. Retrieved from Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Congressional+Voting+Records

Wolberg, W. (1992, 07 15). Breast Cancer Wisconsin (Original) Data Set. Retrieved from Machine Learning Repository: https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Original%25

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