DM828 - Assignment 3: Reinforcement Learning

Pac-Man seeks reward.
Should he eat or should he run?
When in doubt, q-learn.

Introduction

In this project, you will implement q-learning. You will test your agents on and then apply it to a simulated robot controller (Crawler) and Pac-Man.

The code for this project contains the following files, which are available in a zip archive:

Files you will edit

Files you should read but NOT edit

Files you can ignore

What to submit: You will fill in portions of qlearningAgents.py, and analysis.py during the assignment. You should submit only these files. Please don't change any others.

Deadline:

Evaluation: Your code will be autograded for technical correctness. Please do not change the names of any provided functions or classes within the code, or you will wreak the autograder. However, the correctness of your implementation -- not the autograder's output -- will be the final judge of your score.

The grade serves only as a form of feedback and it will not be used for the final grade that depends only by the written exam. For this assignment: if you make an honest effort at question 4 you will pass, otherwise fail. The remaining questions are optional. Questions 1 to 3 have been removed. The points corresponding to a question are left to indicate the level of difficulty.

Getting Help: You are not alone! If you find yourself stuck on something, ask your colleagues or contact the teacher for help. He doesn't know when or how to help unless you ask. But in any case do not ask for code, ask only verbal help. You must implement the required procedures yourself. One more piece of advice: if you don't know what a variable does or what kind of values it takes, print it out.

Q-learning

To get started, run Gridworld in manual control mode, which uses the arrow keys:

python gridworld.py -m

You will see the two-exit layout from class. The blue dot is the agent. Note that when you press up, the agent only actually moves north 80% of the time. Such is the life of a Gridworld agent! 

You can control many aspects of the simulation.  A full list of options is available by running:

 python gridworld.py -h

The default agent moves randomly

 python gridworld.py -g MazeGrid

You should see the random agent bounce around the grid until it happens upon an exit.  Not the finest hour for an AI agent.

Note: The Gridworld MDP is such that you first must enter a pre-terminal state (the double boxes shown in the GUI) and then take the special 'exit' action before the episode actually ends (in the true terminal state called TERMINAL_STATE, which is not shown in the GUI).  If you run an episode manually, your total return may be less than you expected, due to the discount rate (-d to change; 0.9 by default).

Look at the console output that accompanies the graphical output (or use -t for all text). You will be told about each transition the agent experiences (to turn this off, use -q). 

As in Pac-Man, positions are represented by (x,y) Cartesian coordinates and any arrays are indexed by [x][y], with 'north' being the direction of increasing y, etc.  By default, most transitions will receive a reward of zero, though you can change this with the living reward option (-r). 

A value iteration agent does not actually learn from experience.  Rather, it ponders its MDP model to arrive at a complete policy before ever interacting with a real environment.  When it does interact with the environment, it simply follows the precomputed policy (e.g. it becomes a reflex agent). This distinction may be subtle in a simulated environment like a Gridword, but it's very important in the real world, where the real MDP is not available. 

Question 4 You will write a q-learning agent, which does very little on construction, but instead learns by trial and error from interactions with the environment through its update(state, action, nextState, reward) method.  A stub of a q-learner is specified in QLearningAgent in qlearningAgents.py, and you can select it with the option '-a q'. For this question, you must implement the update, getValue, getQValue, and getPolicy methods.

Note: For getValue and getPolicy, you should break ties randomly for better behavior. The random.choice() function will help. In a particular state, actions that your agent hasn't seen before still have a Q-value, specifically a Q-value of zero, and if all the actions that your agent has seen before have a negative Q-value, an unseen action may be optimal.

Important: Make sure that you only access Q values by calling getQValue in your getValue, getPolicy functions. This abstraction will be useful for question 9 when you override getQValue to use features of state-action pairs rather than state-action pairs directly.

With the q-learning update in place, you can watch your q-learner learn under manual control, using the keyboard:

python gridworld.py -a q -k 5 -m

Hint: You may use the util.Counter class in util.py, which is a dictionary with a default value of zero. However, be careful with argMax: the actual argmax you want may be a key not in the counter!

Question 5 (2 points) Complete your q-learning agent by implementing epsilon-greedy action selection in getAction, meaning it chooses random actions epsilon of the time, and follows its current best q-values otherwise.

python gridworld.py -a q -k 100 

You can choose an element from a list uniformly at random by calling the random.choice function. You can simulate a binary variable with probability p of success by using util.flipCoin(p), which returns True with probability p and False with probability 1-p.

Question 6 (1 points) First, train a completely random q-learner with the default learning rate on the noiseless BridgeGrid for 50 episodes and observe whether it finds the optimal policy.

python gridworld.py -a q -k 50 -n 0 -g BridgeGrid -e 1

Question 7 (1 point) With no additional code, you should now be able to run a q-learning crawler robot:

 python crawler.py

This will invoke the crawling robot from class using your q-learner.  Play around with the various learning parameters to see how they affect the agent's policies and actions.   Note that the step delay is a parameter of the simulation, whereas the learning rate and epsilon are parameters of your learning algorithm, and the discount factor is a property of the environment.  

Approximate Q-learning and State Abstraction

Question 8 (1 points) Time to play some Pac-Man! Pac-Man will play games in two phases. In the first phase, training, Pac-Man will begin to learn about the values of positions and actions. Because it takes a very long time to learn accurate q-values even for tiny grids, Pac-Man's training games run in quiet mode by default, with no GUI (or console) display. Once Pac-Man's training is complete, he will enter testing mode. When testing, Pac-Man's self.epsilon and self.alpha will be set to 0.0, effectively stopping q-learning and disabling exploration, in order to allow Pac-Man to exploit his learned policy. Test games are shown in the GUI by default. Without any code changes you should be able to run q-learning Pac-Man for very tiny grids as follows:

 python pacman.py -p PacmanQAgent -x 2000 -n 2010 -l smallGrid 

Hint: If your QLearningAgent works for gridworld.py and crawler.py but does not seem to be learning a good policy for Pac-Man on smallGrid, it may be because your getAction and/or getPolicy methods do not in some cases properly consider unseen actions. In particular, because unseen actions have by definition a Q-value of zero, if all of the actions that have been seen have negative Q-values, an unseen action may be optimal.

Note: If you want to experiment with learning parameters, you can use the option -a, for example -a epsilon=0.1,alpha=0.3,gamma=0.7. These values will then be accessible as self.epsilon, self.gamma and self.alpha inside the agent.

Note: While a total of 2010 games will be played, the first 2000 games will not be displayed because of the option -x 2000, which designates the first 2000 games for training (no output). Thus, you will only see Pac-Man play the last 10 of these games. The number of training games is also passed to your agent as the option numTraining.

Note: If you want to watch 10 training games to see what's going on, use the command:

 python pacman.py -p PacmanQAgent -n 10 -l smallGrid -a
numTraining=10

Make sure you understand what is happening here: the MDP state is the exact board configuration facing Pac-Man, with the now complex transitions describing an entire ply of change to that state. The intermediate game configurations in which Pac-Man has moved but the ghosts have not replied are not MDP states, but are bundled in to the transitions.

Once Pac-Man is done training, he should win very reliably in test games (at least 90% of the time), since now he is exploiting his learned policy.

However, you'll find that training the same agent on the seemingly simple mediumGrid may not work well. In our implementation, Pac-Man's average training rewards remain negative throughout training. At test time, he plays badly, probably losing all of his test games. Training will also take a long time, despite its ineffectiveness.

Pac-Man fails to win on larger layouts because each board configuration is a separate state with separate q-values. He has no way to generalize that running into a ghost is bad for all positions. Obviously, this approach will not scale.

Question 9 (3 points) Implement an approximate q-learning agent that learns weights for features of states, where many states might share the same features. Write your implementation in ApproximateQAgent class in qlearningAgents.py, which is a subclass of PacmanQAgent.

Note: Approximate q-learning assumes the existence of a feature function f(s,a) over state and action pairs, which yields a vector f₁(s,a) .. f_i(s,a) .. f_n(s,a) of feature values. We provide feature functions for you in featureExtractors.py. Feature vectors are util.Counter (like a dictionary) objects containing the non-zero pairs of features and values; all omitted features have value zero.

The approximate q-function takes the following form

By default, ApproximateQAgent uses the IdentityExtractor, which assigns a single feature to every (state,action) pair. With this feature extractor, your approximate q-learning agent should work identically to PacmanQAgent. You can test this with the following command:

 python pacman.py -p ApproximateQAgent -x 2000 -n 2010 -l smallGrid

Important: ApproximateQAgent is a subclass of QLearningAgent, and it therefore shares several methods like getAction. Make sure that your methods in QLearningAgent call getQValue instead of accessing q-values directly, so that when you override getQValue in your approximate agent, the new approximate q-values are used to compute actions.

Once you're confident that your approximate learner works correctly with the identity features, run your approximate q-learning agent with our custom feature extractor, which can learn to win with ease:

 python pacman.py -p ApproximateQAgent -a extractor=SimpleExtractor -x 50 -n 60 -l mediumGrid 

 python pacman.py -p ApproximateQAgent -a extractor=SimpleExtractor -x 50 -n 60 -l mediumClassic 

If you have no errors, your approximate q-learning agent should win almost every time with these simple features, even with only 50 training games.

Congratulations! You have a learning Pac-Man agent!