Project 2: Multi-Agent Search

Project 2: Multi-Agent Search 8

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:
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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.
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
(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:
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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 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. You should submit this file with your code and comments.
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 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.
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Welcome to Multi-Agent Pacman
First, play a game of classic Pacman by running the following command:
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: As features, try the reciprocal of important values (such as distance to
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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.
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(str(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
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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 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
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.
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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 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 tiebreaking 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 alphabeta 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.
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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 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
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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.
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
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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 attu, 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, please upload the following file to Project 2 on
Canvas: multiAgents.py . Please do not upload the files in a zip file or a
directory.
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