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At Cmotions we love to learn from each other and that is why we regularly collaborate on internal projects, in which we can express our creativity, curiosity and eagerness to learn. In this article we want to share what we did in the ‘Snake’ project, where we learned the computer to play snake using Reinforcement Learning. Never heard of Reinforcement Learning before? Not to worry, we’ll start our explanation of this project at the very beginning. Intrigued by this project and curious what our code looks like, we’ve shared that too!

Introduction

You have learned to walk on your feet when you were only 8-15 months old and before you were two years old you could speak your first small sentences. Your parents’ encouragement was probably an important incentive for you to try to walk after falling. And maybe the ability to reach for other things felt like a victory when you stood on your feet for even a moment and helped you to try it over and over again. Not every time you succeeded, but in the end, you learned how to be stable on your feet and move forward. You learned using Reinforcement Learning! We as humans have amazing learning capabilities and when you dedicate your time and energy in any kind of task you can become extremely good at performing this task. Acrobats, musicians and artists are living examples of human expertise.

As humans we are very skilled at gaining new skills based on what we already learned in the past, we’re quite good at generalizing our knowledge to use in new tasks. But we definitely also have our weaknesses, like we are unable to memorize and process huge amounts of information. That is why  we try to program computers to perform these kind of tasks for us. Even though computers have some clear advantages versus humans, it can be difficult to make a computer smart enough to win against a human expert in decision making situations like playing games. In 1996, for the first time, a computer was able to defeat a grandmaster in chess; Kasparov. The computer was able to defeat Kasparov by computing every possible move until there are no more possibilities. This took enormous computing power, but the progress in playing games didn’t end here. Between 2016 and 2019 Computer Algorithms learned to defeat human experts in Go and Chess with a lot less computing power needed. The acceleration in this technology has only grown in the last years with day-to-day implementations such as self-driving cars, robotics and complex strategic games such as Starcraft II and No Limit Holdem Poker.  You might wonder how they did this. Well, remember Reinforcement Learning?

Introduction to Reinforcement Learning

When working on trying to defeat the grandmaster of chess, it was quickly recognized that computing all the possible solutions and choosing the best solution is not a very efficient way to play (and win) a game. Reinforcement Learning came to the stage and very soon was able to prove its effectivity when it comes to playing, and winning, games. With Reinforcement Learning the computer learns to make optimal decisions for the future.

The process of Reinforcement Learning looks like this:

In Reinforcement Learning the computer (agent) takes actions within a given set of rules and possibilities (environment). Actions can lead to a positive encouragement (rewards) or negative encouragement (punishments). By taking an action, the agent is moving from one situation (state) to the next. Moreover, the environment holds, in case of chess, the rules of the game like physical size of the board and possible steps per type of piece. In Reinforcement Learning it’s about taking the best possible action or path to gain maximum rewards and minimum punishment in the future through observations in a specific situation.

In the chess game the state of the game would be the situation on the chess board, meaning where each piece is located on the board. This state gives us a possible action space for each piece, meaning all the possible actions at that moment for each piece on the board, of course keeping in mind the rules of the chess game. When the agent (player) moves a piece, the games reaches a new state. Which also means the possible actions for each piece on the board might change as well. Just like when we play chess ourselves, before the computer decides which move to make, it tries to predict what would be the most valuable move, i.e. which move would lead to winning the game as fast as possible.

Let’s see how this would work for chess. The first image shows the start of the game, the first state, for the knight we show its actionspace, but of course each piece of the board has its own. Let’s assume the agent decides to move the knight. Leading to the second image, and second state, of the game. Also meaning the knight, and other pieces, have an updated actionspace.

Image by Rafael Javier from Pixabay 

Of course, at the beginning of a game it can be quite difficult to predict which move would be the most valuable, but as the game progresses, this is becoming more and more clear and easier to predict. Something every chess player will recognize.

In Reinforcement Learning, the agent starts learning by using trial and error. It remembers which moves were made, how long the game lasted and what the outcome was. Like for ourselves, the more we play, the better we know what a good next move would be, giving the current state of the game. But unlike us, a computer can play games at ligthning speed and has a huge memory to remember every little detail.

In more technical terms, in Reinforcement Learning we can use a algorithm which uses the current state and action (next move) as input and expected reward as output. The goal is to find a suitable action model within the environment in which the agent increases the expected cumulative reward of the agent in the future. The expected cumulative future reward is expressed in a value function. Reinforcement Learning models update their value function by interacting with the environment, choosing an action, looking at the new state, looking at the reward, then updating. With multiple iterations the model will keep learning and we expect this value function to increase, meaning the agent will keep improving at playing (winning) the game.

Choosing the right Reinforcement Learning algorithm

In order to teach our agent to take the best actions in all possible states for acquiring the maximum reward over time, we need to choose a Reinforcement Learning Algorithm (RLA) with which our agent can learn what actions work best in the different states.

We call the collection of these preferred actions in the different states the policy of the agent. In the end, the agent should have a policy that will give her the highest lifetime reward. A large variety of algorithms to find the optimal policy exist and we will group them into three categories to make things understandable:

  1. Model Based
  2. Policy Based
  3. Value Based
Model Based

The first category is that of Model-Based RLA’s, where the algorithm uses a model to predict how the environment reacts to actions, thereby giving the agent ‘understanding’ of what her future state will be if she chooses for a particular action. In Model-Free algorithms, the agent will not have an explicit prediction of what her environment will look like after taking an action. So, although every RLA could be seen as a Machine Learning model for the agent to base its actions upon, the distinction between Model-Based and Model-Free is about whether an explicit (predictive) model about the future state is used or not.

Policy Based

Although not explicitly having an expectation of the future environment, some of these Model-Free algorithms can find the ultimate policy, based on searching for an optimal combination of states and wise actions to take in these states. These are called Policy-Based RLA’s. One of the most common algorithms of this sort is the Policy Gradient Method.

Value Based

Some algorithms go one step deeper than these Policy-Based algorithms by optimizing the expected future reward per state. In doing so, these Value-Based algorithms find the best actions to take in these different states, thereby having a collection of state-action combinations which ultimately make up the policy of the agent in her environment. So, Policy-Based and Value-Based algorithms seem very similar, but the main difference is that policies are stored and updated in Policy-Based algorithms, but in Value-Based algorithms the value function is stored and updated, from which the combinations of states and actions can be derived, and the policy thereby constructed. We will be using such an algorithm: Double Deep Q-Network (Double DQN).

Defining the SNAKE game

Now that we know what Reinforcement Learning is and how it teaches an agent to achieve goals by interacting with its environment, it is time to try it ourselves! Remember the game we used to play in the early 2000’s on our good old Nokia mobile phone? We have all been playing the nostalgic game Snake at least once in our life, right? The goal is simple: being a snake you navigate through a square playground looking for food. As you eat more food, the difficulty increases because your snake will grow longer, and you cannot crash into yourself. Snake is a good choice for a first introduction to Reinforcement Learning, because it lets us define the environment, agent, states, actions and rewards relatively simple.

Our game environment can be defined as a grid of points, with a piece of food at a random coordinate in that grid. In our version of Snake there are no walls, which means that the only way the snake can die is by a collision into its own body. Our agent – the snake – is encoded by a list of coordinates that are covered by the snake, and the state is the current representation of the environment. The picture below shows an example of what the environment could look like. Where the F is food, H is the head of the snake and T is its tail.

For this article, we have experimented with different representations of the state, incorporating various sources of information such as the direction of the snake and the distance to the food. Additionally, we have experimented with adding spatial features extracted by convolutional filters. Convolutional filters extract spatial information of an image by multiplying regions of pixels in an input with weights that are learned by a neural network. This results in a feature mapping that encodes spatial information of the playground, like we will explain more in detail later on.

As the snake navigates through the environment, it can either move up, down, left or right. However, according to the rules of the game, the snake cannot move in the opposite direction of the current direction. Therefore, given the state, we can only take three out of four actions. This subset of actions is what we call the action space. Our goal is, given a certain state, to choose the action that maximizes the future lifetime reward, which can consist of multiple features. In the first place, our snake is rewarded when it eats food, and the score increases. Conversely, the snake is negatively rewarded when it collides into its own body. Additionally, we have included a small penalty to the reward when the snake moves further away from the food, and we added a small positive reward when the snake moves closer to the food. This encourages the snake to pursue eating food instead of only avoiding a collision.

It is very informative to play around with these rewards and punishments, since the result of your decisions on what to reward and what to punish might surprise you from time to time (actually, a lot of the times). For example, before introducing the small rewards and punishments for getting closer to or moving away from the food, the snake would sometimes run in circles in order to survive, thereby not scoring any points. On the contrary, a penalty for walking around for too long without eating, resulted in the snake wanting to commit suicide immediately to avoid “suffering” from walking around without eating. Taking into account how simple the game of snake is, imagine how hard it is to define good rewards and punishments in real life, to avoid “toxic” behaviour.

Now that we know what the actions, rewards and states in our situation are, it’s time to have a look at how we are going to incorporate this in a model that can be trained.

Optimizing Reinforcement Learning

By using a neural network with Python library Tensorflow we estimate the total future rewards of our possible actions given our state. So, given a set of input features, which is the current state, we are going to predict the future rewards given our possible actions. In other words, we are training our neural network by updating our Q function based on the reward for a given action. Such a neural network is called a Deep Q-Network (DQN). This Q-function is the prediction of total future reward for the agent, when choosing action a in state s. The formula representing the way the function is updated is called the “Bellman-equation” and given by:

So, besides the Q function, the equation has parameter alpha as the learning rate of the algorithm that influences how fast the Q function is updated and therefore the rate at which the perception of the agent changes while learning her best actions. Reward function R shows the immediate reward of taking action in state s. Discount rate gamma discounts future rewards that come after the immediate reward. This is necessary to reflect real life, in which a reward in the far future is most of the times deemed (slightly) less important than immediate reward. These hyperparameters alpha and gamma are set by the programmer before the algorithm is deployed.

By learning which actions give us the most future reward in which states, the agent can learn to effectively play snake.

We are going to train two different models with different input features/states in order to compare the performance and complexity of both versions.

Model V1 – a simple model

The first step we must take in building a DQN model is to define the features/states that we will use to predict the Q-values. This is one of the most important steps in setting up a Reinforcement Learning model as it yields all the information the model will use, such that giving too little information will result in a poor model performance. Nonetheless, we do not want to overcomplicate our first model and therefore choose fairly simple input features that contain signals about the location of the food and if there is a snake cell (i.e. her own body) beside the head of the snake.

For the first model we tried to keep the features as easy as possible to understand for our neural network (and ourselves 😉). The features used by this first model are as follows:

  • X-coordinate of the food minus the x-coordinate of the snake’s head.
  • Y-coordinate of the food minus the y-coordinate of the snake’s head.
  • Dummy variable: if there is snake cell below head
  • Dummy variable: if there is snake cell above head
  • Dummy variable: if there is snake cell left of head
  • Dummy variable: if there is snake cell right of head

Based on these features we give the snake information about the location of the food, and immediate danger of a certain choice based on the snake’s body. However, the snake does not have full information about her body and therefore cannot strategically choose actions to avoid being locked by her body later in the game.

For this first version of the model, we insert fairly simple input features that consist of ‘which direction the food is’ and ‘if the snake’s body is near its head’, we do not want to overcomplicate our model. Therefore, we choose to build a neural network consisting of two layers with 16 neurons and end with a dense layer that forecasts the reward for each action. This neural network will then be used as our Q function.

Once the model is set, we want to train the model until it converges to an optimum, which means that we do not see the average reward improve anymore (enough) after a certain number of training iterations. We help the model converge quicker by giving example actions for 20% of the time. This way, the model has enough data about how to gain rewards such that these actions will gain higher Q-values.

For our first version of the model, we find that after around 500.000 training iterations, we don’t see the rewards improve anymore. This takes around 30 to 60 minutes of training, depending on the processor speed.

Model V2 – a more strategic model

As we chose our first model to be fairly simple, it could not look further ahead on the snake’s body to understand the full current state of the game and therefore the snake could be trapped easily inside its body such that it dies. To improve the model, we want to use a convolutional neural network to understand the full picture of the game such that it can make strategic choices so that it will not trap itself.

However, by using convolutional filters to understand the game’s image there is a tradeoff between simplifying the input by aggregating the pixels of the game, such that it will lose precision on the whereabouts of the snake’s body, and size of the network such that the network can understand the many pixels given by the image, where a too large size will make the model so complex that it will take very long to train.

To deal with this problem we create a combined network of the input features from the last model, that gives very precise information about dangers and directions, and combine them with the snake’s snapshot image such that it will give the snake more strategic insights about the state of the game.

In order to let the neural network understand the image, we transform the game into an array of shape: (game width, game height, 3). This array will then have an array with the length of three for each point in the snake’s map, that will be used to indicate if there is a snake body, snake head or food by using dummy variables. For example, if the pixel is filled with a snake’s body, the array will then be given by [1,0,0] and if there is food placed on the pixel the array will be given by [0, 0, 1]. Then, an example of what the full input array for the convolutional layers could be is given by:

Now the input of the DQN model for this version will be a tuple with the state features of our first model’s version and the game state array for the convolutional part of the model. Because of this combination of two parts, it is a Double DQN.

As previously mentioned, the input of the model will be a combined input of model V1 on features and the image as converted to an array. Our model will first split our tuple containing both features by the features array and the convolution array. Once we have our separated array containing the snake’s game snapshot, we will let this go through two separate convolutional layers containing 8 filters, a kernel with size=(4, 4) and strides=2, where the padding is ‘same’ which makes sure that we also account for the border pixels in our model. After the input has gone through both convolutional layers, we will have extracted signals about the game like “there are a lot of body parts in the bottom right corner”, which can help the snake to stay away from there. Flattening this array of signals makes us able to use these signals in a normal dense layer. Next, after flattening the array, we use two dense layers of 256 and 64 neurons to further extract signals about the state of the game.

For the normal features we use one dense layer of 16 neurons to extract signals about immediate threats and the position of the food. The moment comes when we concatenate both the normal signals and our convolutional signals together such that we can use them simultaneously in a dense layer which will finally be used to predict the Q-values for each action.

Next, we train our multi-input model until the model converges to an optimum where the average reward is not improving anymore. As we have a much larger network containing convolutional filters, it will take the algorithm a lot longer to train. Again, we help the model by giving example actions for 20% of the time. Once the model has had a good amount of training loops (around 1 million iterations) this part can be removed to get more exploration observations and have more data to find a good strategy in the training data.

For this second version of the model, we find that it converges after approximately 5 million training iterations which take around 4-7 hours of training, depending on the processor speed.

Results

Finally, we come to the most important part of the project where we assess the performance of our models. To validate the performance, we want our models to play 100 games till the snake dies. Then we are going to compare the average score and the maximum score out of these 100 games to compare the models. Exploration is avoided, which means that the algorithm is never randomly choosing actions. These are the results:

Score V1 Model V2 Model
Avg Score 22.28 27.16
Max Score 47 72

For the model V1 the average score out of 100 games is 22.28 with a maximum of 47 which is not bad for the fact that this model is not able to lookout for threats ahead. However, incorporating the snapshot of the whole game into the model V2 gave us a significant improvement with an average of 27.16 and a maximum of 72. This shows us that the V2 model, the more strategic one, is indeed capable of determining strategies that look ahead to prevent the snake from getting trapped. However, the training time of this model was also significantly longer with 4-7 hours in respect to 30 to 60 minutes. Therefore, we really see a clear trade-off between performance and required training time to reach the optimum. In practice, this is always a hard decision as there is always a better solution, however the question arises: “Is it worth the time?”. From our first model’s output we saw that the performance was not bad either, so was it worth all the trouble to enhance it? For this article it definitely was!

Can you use Reinforcement Learning in your daily life?

Apart from interesting applications of Reinforcement Learning in games, these algorithms can also be used in business to improve how data can create value. Essentially, if decisions must be made about which actions to take given the current situation an organization is in, a Reinforcement Learning agent can be trained to make decisions or at least give advice on what the next best action should be.

One of these scenarios could be when a marketing team should decide whether to include a customer or prospect in a certain campaign and which offer or communication she should receive. For example, the agent here is the digital assistant of the marketeer, state the characteristics of the (potential) customer plus the timestamp and the actions are choosing between the different offers (or no offer at all) and communications. The environment, which is the real world, will give feedback such as clicks on weblinks, conversion or churn. The designer of the Reinforcement Learning Algorithm should then define the rewards corresponding to these events to steer the agent in the right direction for finding its optimal policy.

Another example could be that of personalizing the homepage on a website based on how a visitor is navigating through the website. The agent is not the visitor, but the digital content manager behind the website, who is choosing which banners to show on which places of the homepage (actions), given online navigation history (states) of the visitor and other information if the visitor is logged in with a profile or from cookies. If the visitor clicks on the shown banner, a positive reward is given by the environment, as this click shows the banner is relevant to the visitor and the homepage is being optimized for this type of visitor. The algorithm will find which actions (show a banner) link best to the possible states (collection of navigation history) to compose the policy.

Curious to see our code for both the Reinforcement Learning models, check out our other article!

Matthijs Otten
Data Consultant at Cmotions m.otten@cmotions.nl
Consultant & Data Scientist at Cmotions j.schoonemann@cmotions.nl
Wim Verboom
Senior Consultant w.verboom@cmotions.nl
Thijs van der Velden
Principal Consultant t.v.d.velden@cmotions.nl
Frank van der Bas
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