Project 2 - Multi-Agent Search - COMP 4200/5430: Artificial Intelligence, Spring 2020
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Project 2: Multi-Agent Search (due 3/6 at 11:00pm)
Table of Contents
Introduction
Welcome
Q1: Reflex Agent
Q2: Minimax
Q3: Alpha-Beta Pruning
Q4: Expectimax
Q5: Evaluation Function
Submission
Pacman, now with ghosts.
Minimax, Expectimax,
Evaluation
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:
https://inst.eecs.berkeley.edu/~cs188/sp19/project2.html
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python autograder.py
Note: If your python refers to Python 2.7, you may need to invoke python3
autograder.py (and similarly for all subsequent Python invocations) or create a conda
environment as described in Project 0 (project0.html#Installation).
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/q2/0-small-tree
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 Project 0 for more information about using the autograder.
The code for this project contains the following files, available as a zip archive
(assets/files/multiagent.zip).
Files you'll edit:
multiAgents.py Where all of your multi-agent search agents will reside.
Files you might want to look at:
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.
You don't need to use these for this project, but may find
other functions defined here to be useful.
Supporting files you can ignore:
graphicsDisplay.py Graphics for Pacman
graphicsUtils.py Support for Pacman graphics
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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 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
multiagentTestClasses.py Project 2 specific autograding test classes
Files to Edit and Submit: You will fill in portions of multiAgents.py during the
assignment. Once you have completed the assignment, you will submit a token generated
by submission_autograder.py . 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. 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, section, 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.
Welcome to Multi-Agent Pacman
First, play a game of classic Pacman by running the following command:
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python pacman.py
and using the arrow keys to move. Now, run the provided ReflexAgent in
multiAgents.py
python 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
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):
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: Remember that newFood has the function asList()
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; in later parts
of the project, you'll be evaluating states.
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Note: You may find it useful to view the internal contents of various objects for debugging.
You can do this by printing the objects' string representations. For example, you can print
newGhostStates with print(newGhostStates) .
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
Don't spend too much time on this question, though, as the meat of the project lies ahead.
Question 2 (5 points): Minimax
Now you will write an adversarial search agent in the provided MinimaxAgent class stub
in multiAgents.py . Your minimax agent should work with any number of ghosts, so
you'll have to write an algorithm that is slightly more general than what you've previously
seen in lecture. In particular, your minimax tree will have multiple min layers (one for each
ghost) for every max layer.
Your code should also expand the game tree to an arbitrary depth. Score the leaves of
your minimax tree with the supplied self.evaluationFunction , which defaults to
scoreEvaluationFunction . MinimaxAgent extends MultiAgentSearchAgent , which
gives access to self.depth and self.evaluationFunction . Make sure your minimax
code makes reference to these two variables where appropriate as these variables are
populated in response to command line options.
Important: A single search ply is considered to be one Pacman move and all the ghosts'
responses, so depth 2 search will involve Pacman and each ghost moving two times.
Grading: We will be checking your code to determine whether it explores the correct
number of game states. This is the only reliable way to detect some very subtle bugs in
implementations of minimax. As a result, the autograder will be very picky about how
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many times you call GameState.generateSuccessor . 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
Hint: Implement the algorithm recursively using helper function(s).
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. Lookahead
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
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Make a new agent that uses alpha-beta pruning to more efficiently explore the minimax
tree, in AlphaBetaAgent . Again, your algorithm will be slightly more general than the
pseudocode from lecture, so part of the challenge is to extend the alpha-beta pruning
logic appropriately to multiple minimizer agents.
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, although the actions it selects can vary because of different tie-breaking behavior.
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.
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.
You must not prune on equality in order to match the set of states explored by our
autograder. (Indeed, alternatively, but incompatible with our autograder, would be to also
allow for pruning on equality and invoke alpha-beta once on each child of the root node,
but this will not match the autograder.)
The pseudo-code below represents the algorithm you should implement for this question.
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:
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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 so far 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.
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
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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.
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).
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, when
run with --no-graphics . The autograder is run on EC2, so this machine will have a fair
amount of resources, but your personal computer could be far less performant (netbooks)
or far more performant (gaming rigs).
The additional points for average score and computation time will only be awarded if you
win at least 5 times.
You can try your agent out under these conditions with
python autograder.py -q q5
To run it without graphics, use:
python autograder.py -q q5 --no-graphics
Submission
In order to submit your project, run python submission_autograder.py and submit the
generated token file multiagent.token to the Project 2 assignment on Gradescope.