Description
Introduction
In this assignment, 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.
This assignment includes an autograder for you to grade your solutions on your
machine. This can be run on all questions with the command:
python autograder.py
It can be run for one particular question, such as q2, by:
python autograder.py -q q2
Files you’ll edit:
1. valueIterationAgents.py A value iteration agent for solving known MDPs.
2. qlearningAgents.py Q-learning agents for Gridworld, Crawler and
Pacman.
3. analysis.py A file to put your answers to questions given in the project.
Files you might want to look at:
• 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 to Edit and Submit: You will fill in portions of valueIterationAgents.py,
qlearningAgents.py, and analysis.py during the assignment. Once you have
completed the assignment, you will submit these files to Canvas. Please do not change
the other files in this distribution.
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.
Markov Decision Processes
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 (5 points): Value Iteration
Recall the value iteration state update equation:
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, Vk. In addition to
runValueIteration, implement the following methods for ValueIterationAgent using
Vk .
• 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 Vk is computed
from a fixed vector Vk−1 (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 the book Sutton & Barto in Chapter 4.1 on page 91.
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 should return the synthesized policy πk+1.
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:
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 (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.
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:
• Prefer the close exit (+1), risking the cliff (-10)
• Prefer the close exit (+1), but avoiding the cliff (-10)
• Prefer the distant exit (+10), risking the cliff (-10)
• Prefer the distant exit (+10), avoiding the cliff (-10)
• Avoid both exits and the cliff (so an episode should never terminate)
To see what behavior a set of numbers ends up in, run the following command to see a
GUI:
python gridworld.py -g DiscountGrid -a value –discount [YOUR_DISCOUNT]
–noise [YOUR_NOISE] –livingReward [YOUR_LIVING_REWARD]
To check your answers, run the autograder:
python autograder.py -q q2
question2a() through question2e() 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
2(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.
Question 3 (5 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.
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.
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 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 q3
Question 4 (1 points): 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 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
CMPT 310 – D200 Simon Fraser University
9
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 Qvalue 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!
To grade your answer, run:
python autograder.py -q q4
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 1000 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 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.
