Experimenting with Gradient Descent in Python

For awhile now, the Computer Science department at my University has offered a class for non-CS students called “Data Witchcraft“. The idea, I suppose, is that when you don’t understand how a technology works, it’s essentially “magic“. (And when it has to do with computers and data, it’s dark magic at that.)

But even as someone who writes programs all day long, there are often tools, algorithms, or ideas we use that we don’t really understand–just take at face value, because well, they seem to work, we’re busy, and learning doesn’t seem necessary when the problem is already sufficiently solved.

One of the more prevalent algorithms of this sort is Gradient Descent (GD). The algorithm is both conceptually simple (everyone likes to show rudimentary sketches of a blindfolded stick figure walking down a mountain) and mathematically rigorous (next to those simple sketches, we show equations with partial derivatives across n-dimensional vectors mapped to an arbitrarily sized higher-dimensional space).

Screen Shot 2016-12-15 at 11.54.44 PM.png
Image from course slides

So most often, after learning about GD, you are sent off into the wild to use it, without ever having programmed it from scratch. From this view, Gradient Descent is a sort of incantation we Supreme Hacker Mage Lords can use to solve complex optimization problems whenever our data is in the right format, and we want a quick fix. (Kind of like Neural Networks and “Deep Learning”…) This is practical for most people who just need to get things done. But it’s also unsatisfying for others (myself included).

However, GD can also be implemented in just a few lines of code (even though it won’t be as highly optimized as an industrial-strength version).

That’s why I’m sharing some implementations of both Univariate and generalized Multivariate Gradient Descent written in simple and annotated Python.

Anyone curious about a working implementation (and with some test data in hand) can try this out to experiment. The code snippets below have print statements built in so you can see how your model changes every iteration.

Full Repository

To download and run the full repo, clone it from here:  https://github.com/adpoe/Gradient_Descent_From_Scratch 

But the actual algorithms are also extracted below, for ease of reading.

Univariate Gradient Descent

Requires NumPy.

Also Requires data to be in this this format:  [(x1,y1), (x2,y2) … (xn,yn)], where Y is the actual value.

Multivariate Gradient Descent

Requires NumPy, same as above.

Also Requires data to be in this this format:  [(x1,..xn, y),(x1,..xn, y) …(x1,..xn, y)], where Y is the actual value. Essentially, you can have as many x-variables as you’d like, as long as the y-value is the last element of each tuple.

My data set is included in the full repo. But feel free to try it on your own, if you’re experimenting with this. And enjoy.

Making an AI to Play Flappy Bird w/ Q-Learning


In which I peel back the curtain and outline the innerworkings of a particularly insidious artificial intelligence, whose sole purpose in life is to systematically learn the optimal strategy for a terrifyingly addictive video game, known only to the internet as: Flappy Bird… and in which I also provide code to program a similar AI of your own.

More pointedly, this short post outlines a practical way to get started using a Reinforcement Learning technique called Q-Learning, as applied to a Python Flappy Bird clone, programmed by @TimoWilken.

>> Grab the code base: https://github.com/adpoe/Flappy-AI <<

Humble Beginnings

So you want to beat Flappy Bird, but after awhile it gets tedious. I agree. Instead, why don’t we program an AI to do it for us?  A genius plan, but where do we start?

First, we need a Flappy Bird game to hack upate. The candidate that I suggest is a Python implementation created by Timo Wilken and available for download directly at: https://github.com/TimoWilken/flappy-bird-pygame. This Flappy Bird version is implemented using the PyGame library, which is a dependency going forward.

Here are instructions for PyGame installation. If you get this runing, the hard work is done. (apt-get or homebrew are highly recommended.)

How the Game Works

The first challenge we’ll have in implementing the framework for a Flappy AI is determining exactly how the game workes in its original state.

By using the debugger and stepping through the game’s code during some trial runs, I was able to figure out where key decisions where made, how data flowed into the game, and exactly where I would need to position my AI-agent.

At its basic level, I created an “Agent” class, and passed that class into the running game code. Then, at each loop of the game, I examined the variables available to me, and then passed a ‘MOUSEBUTTONUP’ command to the PyGame event queue whenever the AI decided to jump. Otherwise, I did nothing.

State Representations

From there, the next step was determining a way to model the problem. I decided to use follow the basic guidelines outlined by Sarvagya Vaish, here.

First, I discretized the space in which the bird sat, relative to the next pipe. I was able to get pipe data by accessing the pipe object in the original game code. Similarly, I was able to get bird data by accessing the bird object.

From there, I could determine the location of the bird and the pipes relative to each other. I discretized this space as a 25×25 grid, with the following parameters:

Using this methodology, I created a state tuple that looked like this:

(height_category={0,1,2,3,4}, dist_category={0,1,2,3,4} , collision=True/False)

Then, each iteration of the game loop, I was able to determine the bird’s relative position, and whether it had made a collision with the pipes or not.

If there was no collision, I issued a reward of +1.

If there was a collision, I issued a reward of -1000.

I tried many different state representations here, but mostly it was matter of determining an optimal number of grid spaces and the right parameters for those spaces.

Initially, I started with a 9×9 grid, but moved to 16×16 because I got to a point in 9×9 where I just couldn’t make any more learning progress.

What Works

Very generally, we want to have a tighter grid around the pipes, as this is where most collisions happen. And we want a looser grid as we move outwards. This seemed to give me the best results, as we need different strategies at different locations on the grid.

Exploration Approaches

Our next task is implementing an exploration approach. This is necessary because if we don’t randomly explore the state sometimes, there might be optimal strategies that we are never able to find, simply because we will never be in those states!

Because we have only two choices at any given state (JUMP—or—STAY), implementing exploration was relatively simple.

I started out with a high exploration factor (I used 1/time_value+1), and then I generated a random number between [0,1). If the random number was less than the exploration factor, then I explored.

Over time the exploration factor got lower, and therefore the AI explored less frequently.

Exploration essentially consisted of flipping a fair coin (generating a Boolean value randomly).

  • If true:  then I chose to JUMP.
  • If false:   I chose to STAY.

The main problem I encountered with this method is that the exploration factor was very at the beginning, and sometimes choices were made that were not representative of actual situations that the bird would encounter in ‘true’ gameplay.

BUT, because these decisions were made earlier, they were weighted more heavily in the overall Q-Learning algorithm.

This isn’t ideal, but exploration is necessary, and overall the algorithm works well. So it wasn’t a large problem, overall.

Learning Rates & Their Impact

Very simply, “Learning Rates” dicatate how much we weigh new information about some state over old information. Learning rates can be an value in the range [0,1]. With 0 meaning we never update values (bad), and 1 meaning that we only EVER care about what happened the last time we were in state (short-sighted).

The first learning rate I tried was alpha=(1/time+1). However, this gave very poor results in practice.

This is because time is NOT the most important factor in determining a strategy from any given state. Rather, it is how many times we’ve been to that state.

The problem is that we make extremely poor choices at the beginning of the game (because we simply don’t know any better). But with alpha=(1/time+1), the results of these these poor choices are weighted the most highly.

Once I changed the learning factor to alpha=1/N(s,a), I immediately saw dramatically better results. (That is, where N(s,a) tracks how many times we’ve been in a given state and performed the same action.)


My final, “Smart” bird is the result of about 4 hours of training.

I don’t actually think there would be a way to make the training more efficient, aside from speeding up the gameplay in some way.

Overall, I the results I received from the investment of time I put it in reasonable.

Given more time, I would probably discretize the space even more finely (maybe a 36×36 grid) – so that I could find even more optimal strategies from a more fine-tuned set of positions in the game-space.

How to Use my Smart Bird

To use my smart bird, simply take the following steps:

  1. cd into a directory containing my source code
  2. Ensure that this directory includes the file named ‘txt
  3. Run the command:
    • python flappybird.py “qdata.txt”
  4. Watch Flappy crush it. (the game will run 10x)


Learning From Scratch

Probably more instructive than using my trained bird though, is to simply start training a new bird from scratch. You will see the agony and the ecstasy as he does a terrible number of dumb things, slowly learning how to beat the game.

It’s surprisingly enjoyable (though sometimes frustrating) and highly recommended. Start the process by running:

  • python flappybird.py 

With no other args. Then pass in the ‘qdata.txt’ file next time you run the game, to keep your learning session going.


I consulted the following resources to implement my AI. If you want to do similar work, I’d recommend these resources. These people are much smarter than me. I’m just applying their concepts.

Recursively Parsing a List of Lists into a Game Tree Using Python


I’ve been working on a AI project today and came across this problem.

Given input data structured like so:

[‘A’, [‘B’, (‘D’, 3), (‘E’, 5)], [‘C’, [‘F’, [‘I’,(‘K’,0), (‘L’, 7)],(‘J’,5)], [‘G’, (‘M’,7), (‘N’,8)], (‘H’,4)]]

I need to parse and build tree which has an arbitrary branching factor, and values only at the leaves.

(As for why:  Later, I’ll be running Minimax and some other algorithms on this tree, in order to algorithmically determine the best possible game move. More on that in another post.)

This seemed like a good problem to solve recursively. And to avoid a soul-sucking debug session, I decided my goal was to solve it as succinctly as possible.

Here’s what I came up with. Why I’m posting: This seems like it would be a very common AI/Data-Structures problem, but my first few searches on the subject came up with nada. Nothing even closely related to the problem I’m solving. So doing my part to fix that now.

Working Code

Signing Out

Side note. I’m actually not sure what this tree (with weights only at the leaves) would be called technically. It reminds me of the tree made during Huffman Encoding, but it’s not quite a match for that since we aren’t summing the values in all parent nodes. If you know the technical name, let me know, so I can update.