Description
1 Introduction
In this project, you will design agents for the classic version of Pacman, including ghosts. Along the way,
you will implement both minimax and expectimax search and try your hand at evaluation function design.
The code base has not changed much from the previous project, but please start with a fresh installation,
rather than intermingling files from project 1.
As in project 1, this project includes an autograder for you to grade your answers on your machine. This
can be run on all questions with the command:
python2 autograder.py
It can be run for one particular question, such as q2, by:
python2 autograder.py -q q2
By default, the autograder displays graphics with the -t option, but doesn’t with the -q option. You can
force graphics by using the –graphics flag, or force no graphics by using the –no-graphics flag.
See the autograder tutorial in Assignment 0 for more information about using the autograder.
The code for this project contains the following files, available as a zip archive.
Files you’ll edit:
multiAgents.py Where all of your multi-agent search agents will reside.
Files you can ignore:
pacman.py The main file that runs Pacman games.
This file also describes a Pacman GameState type, which you will use
extensively in this project
game.py The logic behind how the Pacman world works.
This file describes several supporting types like AgentState, Agent, Direction, and Grid.
util.py Useful data structures for implementing search algorithms.
graphicsDisplay.py Graphics for Pacman
graphicsUtils.py Support for Pacman graphics
textDisplay.py ASCII graphics for Pacman
ghostAgents.py Agents to control ghosts
keyboardAgents.py Keyboard interfaces to control Pacman
layout.py Code for reading layout files and storing their contents
autograder.py Assignment autograder
testParser.py Parses autograder test and solution files
testClasses.py General autograding test classes
test_cases/ Directory containing some test cases for each question
multiagentTestClasses.py Assignment 2 specific autograding test classes
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Files to Edit and Submit: You will fill in portions of multiAgents.py during the assignment. You may
also add other functions and code to this file so as to create a modular implementation. You will submit
this file with your modifications. Please do not change the other files in this distribution or submit any of
our original files other than this 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. We will also run
some additional tests on your code, in addition to tests supplied in the zip file. If all checks out with your
code you will receive all of the points indicated by the autograder, and some more for the additional tests.
Getting Help: You are not alone! If you find yourself stuck on something, contact us for help. The
piazza discussion forum will be monitored and questions answered, and you can also ask questions about the
assignment during office hours. If you can’t make our office hours, let us know and we will arrange a different
appointment. We want the assignment to be rewarding and instructional, not frustrating and demoralizing.
But, we don’t know when or how to help unless you ask.
Piazza Discussion: Please be careful not to post spoilers.
What to Submit
You will be using MarkUs to submit your assignment. MarkUs accounts for the course will be soon be set
up. You will submit three files:
Your modified multiAgents.py
A signed copy of the following acknowledgment
Note: In the various parts below we ask a number of questions. You do not have to hand in answers to these
questions, rather these questions are designed to help you understand what is going on with search.
Multi-Agent Pacman
First, play a game of classic Pacman:
python2 pacman.py
Now, run the provided ReflexAgent in multiAgents.py:
python2 pacman.py -p ReflexAgent
Note that it plays quite poorly even on simple layouts:
python pacman.py -p ReflexAgent -l testClassic
Inspect its code (in multiAgents.py) and make sure you understand what it’s doing.
Question 1 (4 points): Reflex Agent
Don’t spend too much time on this question, as the meat of the project lies ahead.
Improve the ReflexAgent in multiAgents.py to play respectably. The provided reflex agent code provides
some helpful examples of methods that query the GameState for information. A capable reflex agent will
have to consider both food locations and ghost locations to perform well. Your agent should easily and
reliably clear the testClassic layout:
python pacman.py -p ReflexAgent -l testClassic
Try out your reflex agent on the default mediumClassic layout with one ghost or two (and animation off to
speed up the display):
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python pacman.py –frameTime 0 -p ReflexAgent -k 1
python pacman.py –frameTime 0 -p ReflexAgent -k 2
How does your agent fare? It will likely often die with 2 ghosts on the default board, unless your evaluation
function is quite good.
Note: As features, try the reciprocal of important values (such as distance to food) rather than just the
values themselves.
Note: The evaluation function you’re writing is evaluating state-action pairs (i.e., how good is it to perform
this action in this state); in later parts of the project, you’ll be evaluating states (i.e., how good is it to be
in this state).
Options: Default ghosts are random; you can also play for fun with slightly smarter directional ghosts using
-g DirectionalGhost. If the randomness is preventing you from telling whether your agent is improving,
you can use -f to run with a fixed random seed (same random choices every game). You can also play
multiple games in a row with -n. Turn off graphics with -q to run lots of games quickly.
Grading: we will run your agent on the openClassic layout 10 times. You will receive 0 points if your agent
times out, or never wins. You will receive 1 point if your agent wins at least 5 times, or 2 points if your
agent wins all 10 games. You will receive an addition 1 point if your agent’s average score is greater than
500, or 2 points if it is greater than 1000. You can try your agent out under these conditions with
python autograder.py -q q1
To run it without graphics, use:
python autograder.py -q q1 –no-graphics
Question 2 (5 points): Minimax
Now you will write an adversarial search agent in the provided MinimaxAgent class stub in multiAgents.py.
Your minimax search must work with any number of ghosts. In particular, for every max layer (where the
pacman moves) your minimax tree will have multiple min layers, one for each ghost.
gameState does not keep track of whose turn it is to play, you will have to keep track of that in your minimax search. In particular, the pacman (MAX) plays first,
followed by each ghost getting a turn; then the pacman plays again, followed by each ghost getting a turn,
etc.
Score the leaves of your minimax tree with the supplied self.evaluationFunction, which defaults to
scoreEvaluationFunction. You will have to implement a depth-bound, so the leaves of your minimax tree
could be either terminal or non-terminal nodes. Hence, self.evaluationFunction will act as the game
utility function, except that it will be called both on terminal and non-terminal nodes.
Terminal nodes are nodes where either gameState.isWin() or gameState.isLose() is true. However, the
leaves of your tree search might also be non-terminal nodes.
Your Minimax (and all other game tree search algorithms you will implement) must utilize a depth-bound.
The depth-bound you must operate under is stored in the variable self.depth. The depth-bound specifies
number of times the pacman (MAX) gets to play. For example, if the depth-bound is 2, then MAX gets
to make 2 moves and all of the ghosts get 2 moves each. When MAX is about to play a 3rd time, your
search will terminate: instead of considering the possible 3rd moves of MAX it will simply return the value
of self.evaluationFunction treating this node as if it was a terminal node. As another example, if the
depth-bound is zero, your search will immediately return the self.evaluationFunction value of the root
node.
Make sure your minimax code makes reference to the two variables, self.depth and self.evaluationFunction
where appropriate as these variables will vary in response to command line options.
Grading: We will be checking your code to determine whether it explores the correct number of game states.
This is the only way reliable way to detect some very subtle bugs in implementations of minimax. As a
result, the autograder will be very picky about how many times you call GameState.generateSuccessor.
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If you call it any more or less than necessary, the autograder will complain. To test and debug your code,
run
python autograder.py -q q2
This will show what your algorithm does on a number of small trees, as well as a pacman game. To run it
without graphics, use:
python autograder.py -q q2 –no-graphics
Hints and Observations
• The correct implementation of minimax will lead to Pacman losing the game in some tests. This is not
a problem: as it is correct behaviour, it will pass the tests.
• The evaluation function for the pacman test in this part is already written (self.evaluationFunction).
You shouldn’t change this function, but recognize that now we’re evaluating *states* rather than actions, as we were for the reflex agent. Look-ahead agents evaluate future states whereas reflex agents
evaluate actions from the current state.
• The minimax values of the initial state in the minimaxClassic layout are 9, 8, 7, -492 for depths 1,
2, 3 and 4 respectively. Note that your minimax agent will often win (665/1000 games for us) despite
the dire prediction of depth 4 minimax.
python pacman.py -p MinimaxAgent -l minimaxClassic -a depth=4
• Pacman is always agent 0, and the agents move in order of increasing agent index.
• All states in minimax should be GameStates, either passed in to getAction or generated via GameState.generateSuccessor.
In this project, you will not be abstracting to simplified states.
• On larger boards such as openClassic and mediumClassic (the default), you’ll find Pacman to be
good at not dying, but quite bad at winning. He’ll often thrash around without making progress. He
might even thrash around right next to a dot without eating it because he doesn’t know where he’d go
after eating that dot. Don’t worry if you see this behavior, question 5 will clean up all of these issues.
• When Pacman believes that his death is unavoidable, he will try to end the game as soon as possible
because of the constant penalty for living. Sometimes, this is the wrong thing to do with random
ghosts, but minimax agents always assume the worst:
python pacman.py -p MinimaxAgent -l trappedClassic -a depth=3
Make sure you understand why Pacman rushes the closest ghost in this case.
Question 3 (5 points): Alpha-Beta Pruning
Make a new agent that uses alpha-beta pruning to more efficiently explore the minimax tree, in AlphaBetaAgent.
Again, your algorithm must use the depth-bound specified in self.depth and evaluate its leaf nodes with
self.evaluationFunction.
You should see a speed-up (perhaps depth 3 alpha-beta will run as fast as depth 2 minimax). Ideally, depth
3 on smallClassic should run in just a few seconds per move or faster.
python pacman.py -p AlphaBetaAgent -a depth=3 -l smallClassic
The AlphaBetaAgent minimax values should be identical to the MinimaxAgent minimax values. Again, the
minimax values of the initial state in the minimaxClassic layout are 9, 8, 7 and -492 for depths 1, 2, 3 and
4 respectively.
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Grading: Because we check your code to determine whether it explores the correct number of states, it
is important that you perform alpha-beta pruning without reordering children. In other words, successor
states should always be processed in the order returned by GameState.getLegalActions. Again, do not
call GameState.generateSuccessor more than necessary.
To test and debug your code, run
python autograder.py -q q3
This will show what your algorithm does on a number of small trees, as well as a pacman game. To run it
without graphics, use:
python autograder.py -q q3 –no-graphics
The correct implementation of alpha-beta pruning will lead to Pacman losing some of the tests. This is not
a problem: as it is correct behaviour, it will pass the tests.
Question 4 (5 points): Expectimax
Minimax and alpha-beta are great, but they both assume that you are playing against an adversary who
makes optimal decisions. As anyone who has ever won tic-tac-toe can tell you, this is not always the case. In
this question you will implement the ExpectimaxAgent, which is useful for modeling probabilistic behavior
of agents who may make suboptimal choices.
As with the search and constraint satisfaction problems covered in this class, the beauty of these algorithms
is their general applicability. To expedite your own development, we’ve supplied some test cases based on
generic trees. You can debug your implementation on small the game trees using the command:
python autograder.py -q q4
Debugging on these small and manageable test cases is recommended and will help you to find bugs quickly.
Make sure when you compute your averages that you use floats. Integer division in Python
truncates, so that 1/2 = 0, unlike the case with floats where 1.0/2.0 = 0.5.
Once your algorithm is working on small trees, you can observe its success in Pacman. Random ghosts are
of course not optimal minimax agents, and so modeling them with minimax search may not be appropriate.
ExpectimaxAgent, will no longer take the min over all ghost actions, but the expectation according to your
agent’s model of how the ghosts act. To simplify your code, assume you will only be running against an
adversary which chooses amongst their getLegalActions uniformly at random.
To see how the ExpectimaxAgent behaves in Pacman, run:
python pacman.py -p ExpectimaxAgent -l minimaxClassic -a depth=3
You should now observe a more cavalier approach in close quarters with ghosts. In particular, if Pacman
perceives that he could be trapped but might escape to grab a few more pieces of food, he’ll at least try.
Investigate the results of these two scenarios:
python pacman.py -p AlphaBetaAgent -l trappedClassic -a depth=3 -q -n 10
python pacman.py -p ExpectimaxAgent -l trappedClassic -a depth=3 -q -n 10
You should find that your ExpectimaxAgent wins about half the time, while your AlphaBetaAgent always
loses. Make sure you understand why the behavior here differs from the minimax case.
The correct implementation of expectimax will lead to Pacman losing some of the tests. This is not a
problem: as it is correct behaviour, it will pass the tests.
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Question 5 (6 points): Evaluation Function
Write a better evaluation function for pacman in the provided function betterEvaluationFunction. The
evaluation function should evaluate states, rather than actions like your reflex agent evaluation function did.
You may use any tools at your disposal for evaluation, including your search code from the last project.
With depth 2 search, your evaluation function should clear the smallClassic layout with one random ghost
more than half the time and still run at a reasonable rate (to get full credit, Pacman should be averaging
around 1000 points when he’s winning).
python autograder.py -q q5
Grading: the autograder will run your agent on the smallClassic layout 10 times. We will assign points
to your evaluation function in the following way:
• If you win at least once without timing out the autograder, you receive 1 points. Any agent not
satisfying these criteria will receive 0 points.
• +1 for winning at least 5 times, +2 for winning all 10 times
• +1 for an average score of at least 500, +2 for an average score of at least 1000 (including scores on
lost games)
• +1 if your games take on average less than 30 seconds on the autograder machine. The autograder is
run on the cslinux machine which has a fair amount of resources, but your personal computer could be
far less performant (netbooks) or far more performant (gaming rigs). You can use your cslinux login
to run your program on the school machines.
• The additional points for average score and computation time will only be awarded if you win at least
5 times.
Hints and Observations
• As for your reflex agent evaluation function, you may want to use the reciprocal of important values
(such as distance to food) rather than the values themselves.
• One way you might want to write your evaluation function is to use a linear combination of features.
That is, compute values for features about the state that you think are important, and then combine
those features by multiplying them by different values and adding the results together. You might
decide what to multiply each feature by based on how important you think it is.
Academic Honesty
We are aware that solutions to the original Berkeley project exist on the internet. Do not use these solutions
as this would be plagiarism. To earn marks on this assignment you must develop your own solutions. Also
please consider the following points.
• You are to implement the search algorithms presented in the course. These algorithms differ in subtle
but important ways from other presentations of this material. If you implement your search based on
other non-course material it might give the wrong answers. If you try to use solutions found on the
internet the same problem might occur.
• We will check for answers that would arise from solutions to the original Berkeley project. Such answers
indicate that your solution is incorrect, reproducing the errors of the Berkeley lectures. This will cause
you to fail some of our additional tests and you will lose marks for those tests.
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• If we find evidence of plagiarism we will investigate thoroughly and we will send your case to the
University Academic Offenses Office.
• Please do not implement your own ”improvement” to the search algorithms: it will wreak havoc with
the automarker. (Note, if you have invented a significant improvement we would be happy to hear
about it, but don’t use it in this assignment).
• You will be asked to write, sign, scan, and submit a statement acknowledging that the code you
submitted was written by you.
• Although the assignment includes an autograder, additional tests will be run on your code after submission.
Working successfully in a pair
You may work in pairs for this assignment.
If you are working with a partner, make sure that you are actually working together. Your goal should be for
the two of you to help each other learn the material and to avoid getting stuck with frustrating errors. If you
split up the assignment and work separately, you are not getting practice on all aspects of the assignment.
Sometimes a student who is working with a partner drops the course or becomes ill in the middle of an
assignment. If this happens, the other partner is still responsible for completing the assignment on time. If
he or she has been actively engaged in the entire assignment, this should not be a problem; the assignments
are designed so that an individual student can complete them. However, if the remaining partner has not
been actively involved or does not have copies of all of the work, they will have serious difficulty completing
the assignment. Make sure you don’t find yourself in this situation: Be active in all parts of the assignment,
and make sure that at the end of each meeting, both partners have a copy of all of the work.
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