Project 3: For the Love of MDPs

CSE 473 Project 3: For the Love of MDPs and Reinforcement Learning

CSE 473 Project 3: For the Love of MDPs and
Reinforcement Learning
(100 points)
Pac-Man's after reward at every turn,
But should he eat or should he run?
Finding policies with MDPs can be fun
But when you got no model, you gotta q-learn.
Introduction
In this project, you will implement value iteration and q-learning. You will test your agents first on
Gridworld (from class), then apply them 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
valueIterationAgents.py A value iteration agent for solving known MDPs.
qlearningAgents.py Q-learning agents for Gridworld, Crawler and Pac-Man
analysis.py A file to put your answers to questions given in the project.
Files you should read but NOT edit
mdp.py Defines methods on general MDPs.
learningAgents.py Defines the base classes ValueEstimationAgent and
QLearningAgent, which your agents will extend.
util.py Utilities, including util.Counter, which is particularly useful for qlearners.
gridworld.py The Gridworld implementation
featureExtractors.py Classes for extracting features on (state,action) pairs. Used for the
approximate q-learning agent (in qlearningAgents.py).
Files you can ignore
environment.py Abstract class for general reinforcement learning
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environments. Used by gridworld.py.
graphicsGridworldDisplay.py Gridworld graphical display.
graphicsUtils.py Graphics utilities.
textGridworldDisplay.py Plug-in for the Gridworld text interface.
crawler.py The crawler code and test harness. You will run this but not
edit it.
graphicsCrawlerDisplay.py GUI for the crawler robot.
What to submit: You will fill in portions of valueIterationAgents.py, qlearningAgents.py, and
analysis.py during the assignment. You should submit only these files. Please don't change any
others. Submit your files containing code and comments to the CSE 473 Dropbox.
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 havoc on the
autograder. However, the correctness of your implementation -- not the autograder's judgements -
- will be the final judge of your score. If necessary, we will review and grade assignments
individually to ensure that you receive due credit for your work.
No code sharing or copying please! We will be checking your code against other submissions in
the class for logical redundancy. If you copy someone else's code and submit it with minor
changes, we will know. These cheat detectors are quite hard to fool, so please don't try. We trust
you all to submit your own work only; so please don't let us down.
Getting Help: You are not alone! Feel free to use the class discussion board to discuss or get
clarifications on homework-related issues. If you find yourself stuck on something, go to office
hours or email the course staff for help. If you can't make our office hours, let us know and we will
schedule more. We want these projects to be rewarding and instructional, not frustrating and
demoralizing. But, we don't know when or how to help unless you ask. One more piece of advice: if
you don't know what a variable does or what kind of values it takes, print it out to see how it
behaves.
MDPs
To get started, run Gridworld in manual control mode, which uses the arrow keys:
python gridworld.py -m
You will see the two-exit grid layout from the lecture slides. 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
CSE 473 Project 3: For the Love of MDPs and Reinforcement Learning
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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).
Question 1 (20 points) Write a value iteration agent in ValueIterationAgent, which has been
partially specified for you in valueIterationAgents.py. Your value iteration agent is an offline
planner, not a reinforcement agent, and so the relevant training option is the number of iterations
of value iteration it should run (option -i) in its initial planning phase. ValueIterationAgent
takes an MDP on construction and runs value iteration for the specified number of iterations before
the constructor returns.
Value iteration computes k-step estimates of the optimal values, Vk. In addition to running value
iteration, implement the following methods for ValueIterationAgent using Vk.
getValue(state) returns the value of a state.
getPolicy(state) returns the best action according to computed values.
getQValue(state, action) returns the q-value of the (state, action) pair.
These quantities are all displayed in the GUI: values are numbers in squares, q-values are numbers
in square quarters, and policies are arrows out from each square.
Important: Use the "batch" version of value iteration where each vector Vk is computed from a fixed
previous vector Vk-1 (like in lecture), i.e., use two arrays, one for the old values and one for the
new values, and compute the new values one by one from the old values without the old values
being changed.
Note: A policy synthesized from values of depth k (which reflect the next k rewards) will actually
reflect the next k+1 rewards (i.e. you return πk+1). Similarly, the q-values will also reflect one
more reward than the values (i.e. you return Qk+1). You may assume that 100 iterations is enough
for convergence in the questions below.
The following command loads your ValueIterationAgent, which will compute a policy and execute
it 10 times. Press a key to cycle through values, q-values, and the simulation. You should find that
the value of the start state (V(start)) and the empirical resulting average reward are quite close.
python gridworld.py -a value -i 100 -k 10
Hint: On the default BookGrid, running value iteration for 5 iterations should give you this output:
python gridworld.py -a value -i 5
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Your value iteration agent will be graded on a new grid. We will check your values, q-values, and
policies after fixed numbers of iterations and at convergence (e.g. after 100 iterations).
Hint: Use the util.Counter class in util.py, which is a dictionary with a default value of zero.
Methods such as totalCount should simplify your code. However, be careful with argMax: the
actual argmax you want may be a key not in the counter!
Question 2 (5 points) On BridgeGrid with the default discount of 0.9 and the default noise of
0.2, the optimal policy does not cross the bridge. Change only ONE of the discount and noise
parameters so that the optimal policy causes the agent to attempt to cross the bridge. Put your
answer in question2() of analysis.py. (Noise refers to how often an agent ends up in an
unintended successor state when they perform an action.) The default corresponds to:
python gridworld.py -a value -i 100 -g BridgeGrid --discount
0.9 --noise 0.2
Question 3 (15 points) Consider the DiscountGrid layout, shown below. This grid has two
terminal states with positive payoff (shown in green), a close exit with payoff +1 and a distant exit
with payoff +10. The bottom row of the grid consists of terminal states with negative payoff
(shown in red); each state in this "cliff" region has payoff -10. The starting state is the yellow
square. We distinguish between two types of paths: (1) paths that "risk the cliff" and travel near
the bottom row of the grid; these paths are shorter but risk earning a large negative payoff, and
are represented by the red arrow in the figure below. (2) paths that "avoid the cliff" and travel
along the top edge of the grid. These paths are longer but are less likely to incur huge negative
payoffs. These paths are represented by the green arrow in the figure below.
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For each of the following optimal policy types (a) through (e), give an assignment of parameter
values for discount, noise, and livingReward which produce the policy or state that the policy is
impossible by returning the string 'NOT POSSIBLE'. The default corresponds to:
python gridworld.py -a value -i 100 -g DiscountGrid --
discount 0.9 --noise 0.2 --livingReward 0.0
a. Prefer the close exit (+1), risking the cliff (-10)
b. Prefer the close exit (+1), but avoiding the cliff (-10)
c. Prefer the distant exit (+10), risking the cliff (-10)
d. Prefer the distant exit (+10), avoiding the cliff (-10)
e. Avoid both exits (also avoiding the cliff)
question3a() through question3e() should each return a 3-item tuple of (discount, noise, living
reward) in analysis.py.
Note: You can check your policies in the GUI. For example, using a correct answer to 3(a), the
arrow in (0,1) should point east, the arrow in (1,1) should also point east, and the arrow in (2,1)
should point north.
Q-learning
Note that your 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 (20 points) You will now 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 of 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
Recall that -k will control the number of episodes your agent gets to learn. Watch how the agent
learns about the state it was just in, not the one it moves to, and "leaves learning in its wake."
Question 5 (10 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
Your final q-values should resemble those of your value iteration agent, especially along welltraveled paths. However, your average returns will be lower than the q-values predict because of
the random actions and the initial learning phase.
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
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returns True with probability p and False with probability 1-p.
Question 6 (5 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
Now try the same experiment with an epsilon of 0. Is there an epsilon and a learning rate for which
it is highly likely (greater than 99%) that the optimal policy will be learned after 50 iterations?
question6() should return EITHER a 2-item tuple of (epsilon, learning rate) OR the string
'NOT POSSIBLE' if there is none. Epsilon is controlled by -e, learning rate by -l.
Question 7 (5 points) With no additional code, you should now be able to run a q-learning crawler
robot:
python crawler.py
If this doesn't work, you've probably written some code too specific to the GridWorld problem and
you should make it more general to all MDPs. You will receive full credit if the command above
works without exceptions.
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 (5 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
Note that PacmanQAgent is already defined for you in terms of the QLearningAgent you've already
written. PacmanQAgent is only different in that it has default learning parameters that are more
effective for the Pac-Man problem (epsilon=0.05, alpha=0.2, gamma=0.8). You will receive full
credit for this question if the command above works without exceptions and your agent wins at
least 80% of the last 10 runs.
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
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numTraining=10
During training, you will see output every 100 games with statistics about how Pac-Man is faring.
Epsilon is positive during training, so Pac-Man will play poorly even after having learned a good
policy: this is because he occasionally makes a random exploratory move into a ghost. As a
benchmark, it should take about 1,000 games before Pac-Man's rewards for a 100 episode
segment becomes positive, reflecting that he's started winning more than losing. By the end of
training, it should remain positive and be fairly high (between 100 and 350).
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 (15 points) To allow scaling to larger grids, 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) .. fi(s,a) .. fn(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
where each weight wi is associated with a particular feature fi(s,a). In your code, you should
implement the weight vector as a dictionary mapping features (which the feature extractors will
return) to weight values. You will update your weight vectors similarly to how you updated qvalues:
Note that the correction term is the same as in normal Q-Learning.
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
CSE 473 Project 3: For the Love of MDPs and Reinforcement Learning
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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
Even much larger layouts should be no problem for your ApproximateQAgent. (warning: this may
take a few minutes to train)
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!