Project 3: Reinforcement Learning

Project 3: Reinforcement Learning 
Table of Contents
Introduction
Welcome
Q1: Value Iteration
Q2: Bridge Crossing Analysis
Q3: Policies
Q4: Asynchronous Value Iteration
Q5: Prioritized Sweeping Value Iteration
Q6: Q-Learning
Q7: Epsilon Greedy
Q8: Bridge Crossing Revisited
Q9: Q-Learning and Pacman
Q10: Approximate Q-Learning
Submission
Pacman seeks reward.
Should he eat or should he run?
When in doubt, 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 Pacman.
As in previous projects, this project includes an autograder for you to grade
your solutions on your machine. This can be run on all questions with the
command:
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
1 of 18 2/16/20, 4:38 PM
python autograder.py
It can be run for one particular question, such as q2, by:
python autograder.py -q q2
It can be run for one particular test by commands of the form:
python autograder.py -t test_cases/q2/1-bridge-grid
The code for this project contains the following files, available as a zip archive
(files/reinforcement.zip).
Files you'll edit:
valueIterationAgents.py A value iteration agent for solving known MDPs.
qlearningAgents.py Q-learning agents for Gridworld, Crawler and
Pacman.
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 Q-learners.
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
environments. Used by gridworld.py .
graphicsGridworldDisplay.py Gridworld graphical display.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
2 of 18 2/16/20, 4:38 PM
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.
autograder.py Project autograder
testParser.py Parses autograder test and solution files
testClasses.py General autograding test classes
test_cases/ Directory containing the test cases for each
question
reinforcementTestClasses.py Project 3 specific autograding test classes
Files to Edit and Submit: You will fill in portions of valueIterationAgents.py ,
qlearningAgents.py , and analysis.py during the assignment. Please do not
change the other files in this distribution or submit any of our original files
other than these file.
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.
Academic Dishonesty: 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; please don't let us down. If you do, we will pursue the strongest
consequences available to us.
Getting Help: You are not alone! If you find yourself stuck on something,
contact the course staff for help. Office hours and the discussion forum are
there for your support; please use them. 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.
Discussion: Please be careful not to post spoilers.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
3 of 18 2/16/20, 4:38 PM
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 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 Pacman, 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 (4 points): Value Iteration
Recall the value iteration state update equation:
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
4 of 18 2/16/20, 4:38 PM
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 learning 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, V . In addition
to running value iteration, implement the following methods for
ValueIterationAgent using V .
computeActionFromValues(state) computes the best action according to the
value function given by self.values .
computeQValueFromValues(state, action) returns the Q-value of the (state,
action) pair given by the value function given by self.values .
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 V is
computed from a fixed vector V (like in lecture), not the "online" version
where one single weight vector is updated in place. This means that when a
state's value is updated in iteration k based on the values of its successor
states, the successor state values used in the value update computation should
be those from iteration k-1 (even if some of the successor states had already
been updated in iteration k). The difference is discussed in Sutton & Barto
(http://www.cs.ualberta.ca/~sutton/book/ebook/node41.html) in the 6th
paragraph of chapter 4.1.
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 ).
Similarly, the Q-values will also reflect one more reward than the values (i.e.
you return Q ).
You should return the synthesized policy .
Hint: You may optionally 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!
Note: Make sure to handle the case when a state has no available actions in an
MDP (think about what this means for future rewards).
To test your implementation, run the autograder:
k
k
k
k-1
πk+1
k+1
πk+1
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
5 of 18 2/16/20, 4:38 PM
python autograder.py -q q1
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) ,
which you can read off of the GUI) and the empirical resulting average reward
(printed after the 10 rounds of execution finish) 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
Grading: 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).
Question 2 (1 point): Bridge Crossing Analysis
BridgeGrid is a grid world map with the a low-reward terminal state and a
high-reward terminal state separated by a narrow "bridge", on either side of
which is a chasm of high negative reward. The agent starts near the low-reward
state. 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:
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
6 of 18 2/16/20, 4:38 PM
python gridworld.py -a value -i 100 -g BridgeGrid --discount 0.9 --noise 0.2
Grading: We will check that you only changed one of the given parameters, and
that with this change, a correct value iteration agent should cross the bridge.
To check your answer, run the autograder:
python autograder.py -q q2
Question 3 (5 points): Policies
Consider the DiscountGrid layout, shown below. This grid has two terminal
states with positive payoff (in the middle row), 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.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
7 of 18 2/16/20, 4:38 PM
In this question, you will choose settings of the discount, noise, and living
reward parameters for this MDP to produce optimal policies of several different
types. Your setting of the parameter values for each part should have the
property that, if your agent followed its optimal policy without being
subject to any noise, it would exhibit the given behavior. If a particular
behavior is not achieved for any setting of the parameters, assert that the policy
is impossible by returning the string 'NOT POSSIBLE' .
Here are the optimal policy types you should attempt to produce:
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 and the cliff (so an episode should never terminate)
To check your answers, run the autograder:
python autograder.py -q q3
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.
Note: On some machines you may not see an arrow. In this case, press a button
on the keyboard to switch to qValue display, and mentally calculate the policy
by taking the arg max of the available qValues for each state.
Grading: We will check that the desired policy is returned in each case.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
8 of 18 2/16/20, 4:38 PM
Question 4 (1 point): Asynchronous Value Iteration
Write a value iteration agent in AsynchronousValueIterationAgent , which has
been partially specified for you in valueIterationAgents.py . Your value
iteration agent is an offline planner, not a reinforcement learning 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.
AsynchronousValueIterationAgent takes an MDP on construction and runs
cyclic value iteration (described in the next paragraph) for the specified number
of iterations before the constructor returns. Note that all this value iteration
code should be placed inside the constructor ( __init__ method).
The reason this class is called AsynchronousValueIterationAgent is because we
will update only one state in each iteration, as opposed to doing a batch-style
update. Here is how cyclic value iteration works. In the first iteration, only
update the value of the first state in the states list. In the second iteration, only
update the value of the second. Keep going until you have updated the value of
each state once, then start back at the first state for the subsequent iteration. If
the state picked for updating is terminal, nothing happens in that
iteration. You can implement it as indexing into the states variable defined in
the code skeleton.
As a reminder, here's the value iteration state update equation:
Value iteration iterates a fixed-point equation, as discussed in class. It is also
possible to update the state values in different ways, such as in a random order
(i.e., select a state randomly, update its value, and repeat) or in a batch style (as
in Q1). In Q4, we will explore another technique.
AsynchronousValueIterationAgent inherits from ValueIterationAgent from Q1,
so the only method you need to implement is runValueIteration . Since the
superclass constructor calls runValueIteration , overriding it is sufficient to
change the agent's behavior as desired.
Note: Make sure to handle the case when a state has no available actions in an
MDP (think about what this means for future rewards).
To test your implementation, run the autograder. It should take less than a
second to run. If it takes much longer, you may run into issues later in
the project, so make your implementation more efficient now.
python autograder.py -q q4
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
9 of 18 2/16/20, 4:38 PM
The following command loads your AsynchronousValueIterationAgent in the
Gridworld, 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) , which you can read off of the GUI) and the
empirical resulting average reward (printed after the 10 rounds of execution
finish) are quite close.
python gridworld.py -a asynchvalue -i 1000 -k 10
Grading: 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 1000 iterations).
Question 5 (3 points): Prioritized Sweeping Value
Iteration
You will now implement PrioritizedSweepingValueIterationAgent , which has
been partially specified for you in valueIterationAgents.py . Note that this class
derives from AsynchronousValueIterationAgent , so the only method that needs
to change is runValueIteration , which actually runs the value iteration.
Prioritized sweeping attempts to focus updates of state values in ways that are
likely to change the policy.
For this project, you will implement a simplified version of the standard
prioritized sweeping algorithm, which is described in this paper
(http://papers.nips.cc/paper/651-memory-based-reinforcement-learningefficient-computation-with-prioritized-sweeping.pdf). We've adapted this
algorithm for our setting. First, we define the predecessors of a state s as all
states that have a nonzero probability of reaching s by taking some action a .
Also, theta , which is passed in as a parameter, will represent our tolerance for
error when deciding whether to update the value of a state. Here's the
algorithm you should follow in your implementation.
Compute predecessors of all states.
Initialize an empty priority queue.
For each non-terminal state s , do: (note: to make the autograder work for
this question, you must iterate over states in the order returned by
self.mdp.getStates() )
Find the absolute value of the difference between the current value of s
in self.values and the highest Q-value across all possible actions from s
(this represents what the value should be); call this number diff . Do NOT
update self.values[s] in this step.
Push s into the priority queue with priority -diff (note that this is
negative). We use a negative because the priority queue is a min heap,
but we want to prioritize updating states that have a higher error.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
10 of 18 2/16/20, 4:38 PM
For iteration in 0, 1, 2, ..., self.iterations - 1 , do:
If the priority queue is empty, then terminate.
Pop a state s off the priority queue.
Update s 's value (if it is not a terminal state) in self.values .
For each predecessor p of s , do:
Find the absolute value of the difference between the current value
of p in self.values and the highest Q-value across all possible
actions from p (this represents what the value should be); call this
number diff . Do NOT update self.values[p] in this step.
If diff > theta , push p into the priority queue with priority -diff
(note that this is negative), as long as it does not already exist in the
priority queue with equal or lower priority. As before, we use a
negative because the priority queue is a min heap, but we want to
prioritize updating states that have a higher error.
A couple of important notes on implementation:
When you compute predecessors of a state, make sure to store them in a set,
not a list, to avoid duplicates.
Please use util.PriorityQueue in your implementation. The update method in
this class will likely be useful; look at its documentation.
To test your implementation, run the autograder. It should take about 1 second
to run. If it takes much longer, you may run into issues later in the
project, so make your implementation more efficient now.
python autograder.py -q q5
You can run the PrioritizedSweepingValueIterationAgen in the Gridworld using
the following command.
python gridworld.py -a priosweepvalue -i 1000
Grading: Your prioritized sweeping 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 1000 iterations).
Question 6 (4 points): 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.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
11 of 18 2/16/20, 4:38 PM
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 , computeValueFromQValues , getQValue , and computeActionFromQValues
methods.
Note: For computeActionFromQValues , 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 in your computeValueFromQValues and
computeActionFromQValues functions, you only access Q values by calling
getQValue . This abstraction will be useful for question 10 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." Hint: to help with debugging, you can turn
off noise by using the --noise 0.0 parameter (though this obviously makes
Q-learning less interesting). If you manually steer Pacman north and then east
along the optimal path for four episodes, you should see the following Q-values:
Grading: We will run your Q-learning agent and check that it learns the same
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
12 of 18 2/16/20, 4:38 PM
Q-values and policy as our reference implementation when each is presented
with the same set of examples. To grade your implementation, run the
autograder:
python autograder.py -q q6
Question 7 (2 points): Epsilon Greedy
Complete your Q-learning agent by implementing epsilon-greedy action
selection in getAction , meaning it chooses random actions an epsilon fraction
of the time, and follows its current best Q-values otherwise. Note that choosing
a random action may result in choosing the best action - that is, you should not
choose a random sub-optimal action, but rather any random legal action.
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 .
After implementing the getAction method, observe the following behavior of
the agent in gridworld (with epsilon = 0.3).
python gridworld.py -a q -k 100
Your final Q-values should resemble those of your value iteration agent,
especially along well-traveled 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 also observe the following simulations for different epsilon values. Does
that behavior of the agent match what you expect?
python gridworld.py -a q -k 100 --noise 0.0 -e 0.1
python gridworld.py -a q -k 100 --noise 0.0 -e 0.9
To test your implementation, run the autograder:
python autograder.py -q q7
With no additional code, you should now be able to run a Q-learning crawler
robot:
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
13 of 18 2/16/20, 4:38 PM
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.
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.
Question 8 (1 point): Bridge Crossing Revisited
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? question8() in analysis.py 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 .
Note: Your response should be not depend on the exact tie-breaking mechanism
used to choose actions. This means your answer should be correct even if for
instance we rotated the entire bridge grid world 90 degrees.
To grade your answer, run the autograder:
python autograder.py -q q8
Question 9 (1 point): Q-Learning and Pacman
Time to play some Pacman! Pacman will play games in two phases. In the first
phase, training, Pacman 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, Pacman's training games run in quiet mode by default, with no GUI
(or console) display. Once Pacman's training is complete, he will enter testing
mode. When testing, Pacman's self.epsilon and self.alpha will be set to 0.0,
effectively stopping Q-learning and disabling exploration, in order to allow
Pacman to exploit his learned policy. Test games are shown in the GUI by
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
14 of 18 2/16/20, 4:38 PM
default. Without any code changes you should be able to run Q-learning Pacman
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 Pacman 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 time. The autograder will run 100 test games after the 2000
training games.
Hint: If your QLearningAgent works for gridworld.py and crawler.py but does
not seem to be learning a good policy for Pacman on smallGrid , it may be
because your getAction and/or computeActionFromQValues 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. Beware of the
argmax function from util.Counter!
Note: To grade your answer, run:
python autograder.py -q q9
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 Pacman 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
During training, you will see output every 100 games with statistics about how
Pacman is faring. Epsilon is positive during training, so Pacman 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 between
1,000 and 1400 games before Pacman's rewards for a 100 episode segment
becomes positive, reflecting that he's started winning more than losing. By the
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
15 of 18 2/16/20, 4:38 PM
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 Pacman, with the now complex transitions
describing an entire ply of change to that state. The intermediate game
configurations in which Pacman has moved but the ghosts have not replied are
not MDP states, but are bundled in to the transitions.
Once Pacman 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 will find that training the same agent on the seemingly simple
mediumGrid does not work well. In our implementation, Pacman'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.
Pacman 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 10 (3 points): Approximate Q-Learning
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 f (s,a) .. f (s,a) .. f (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 nonzero pairs of features and values; all omitted features have value zero.
The approximate Q-function takes the following form
where each weight w is associated with a particular feature f (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 Q-values:
1 i n
Q(s, a) =
n
∑
i=1
fi(s, a)wi
i i
wi ← wi + α ⋅ difference ⋅ fi(s, a)
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
16 of 18 2/16/20, 4:38 PM
Note that the term is the same as in normal Q-learning, and is the
experienced reward.
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
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.
Grading: We will run your approximate Q-learning agent and check that it
learns the same Q-values and feature weights as our reference implementation
when each is presented with the same set of examples. To grade your
implementation, run the autograder:
python autograder.py -q q10
Congratulations! You have a learning Pacman agent!
Submission
difference = (r + γ max
a′
Q(s′
, a′
)) − Q(s, a)
difference r
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
17 of 18 2/16/20, 4:38 PM
In order to submit your project, please upload the following file to Project 3 on
Canvas: qLearningAgents.py , valueIterationAgents.py , and analysis.py .
Please do not upload the files in a zip file or a directory.
CSE 573: Introduction to Artificial Intelligence, W... https://courses.cs.washington.edu/courses/cse57...
18 of 18 2/16/20, 4:38 PM