Project 2: Multi-Agent Pacman

Table of Contents

• Introduction
• Welcome
• Q1: Reflex Agent
• Q2: Minimax
• Q3: Alpha-Beta Pruning
• Q4: Expectimax
• Q5: Evaluation Function
• Extra Credit: Contest

Pacman, now with ghosts.
Minimax, Expectimax,
Evaluation.

Introduction

In this project, your team 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.

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:

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/q2/0-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.

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. You can, however, use your search.py and searchAgents.py in any way you want.

The code for this project contains the following files, available as a zip archive.

Key files to read

Files you can ignore

What to submit: You will fill in portions of multiAgents.py during the assignment. You should submit this file with your code and comments. You should also submit supporting files (like search.py, etc.) that you use in your code. Please do not change the other files in this distribution or submit any of the original files in the distribution other than multiAgents.py.

Please use turnin to submit your work. Each team should submit only one copy.

In addition, please send me an email with the following information:

• the names of both members of the team and
• the name under which the work has been submitted.

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, clarity, and creativity of your implementation -- not the autograder's judgements -- will be the final judge of your score. Don't forget: I will meet with some of you for code reviews to discuss your work in detail.

Multi-Agent Pacman

First, play a game of classic Pacman:

python pacman.py

python pacman.py -p ReflexAgent

python pacman.py -p ReflexAgent -l testClassic

Question 1 (5 points)  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

python pacman.py --frameTime 0 -p ReflexAgent -k 1

python pacman.py --frameTime 0 -p ReflexAgent -k 2

Note: you can never have more ghosts than the layout permits.

Note: As features, try the reciprocals 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.

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: I 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, 2 points if your agent wins at least 8 times, or 3 points if your agent wins all 10 games. You will receive an additional 1 point if your agent's average score is greater than 500. If your agent's average score is greater than 1000, I'll give you one more point. 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) 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 appears in the textbook. 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: Here we'll say that a full move in the search tree is one Pacman move and all the ghosts' responses, so depth 2 search will involve Pacman and each ghost moving two times.

Grading: I 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.getLegalActions. If you call it any more or less than necessary, the autograder will complain. Note, however, that the autograder will accept solutions both with and without the Directions.STOP action available. 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 behavior, it will pass the tests.
• The evaluation function in this part is already written (self.evaluationFunction). You shouldn't change this function, but recognize that now you're evaluating *states* rather than actions, as you 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 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.
• 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) 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 pseudo-code in the textbook, 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).

python pacman.py -p AlphaBetaAgent -a depth=4 -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 the autograder checks 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 the autograder. (Indeed, alternatively, but incompatible with the 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.)

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 behavior, it will pass the tests.

Question 4 (5 points) Random ghosts are of course not optimal minimax agents, and so modeling them with minimax search may not be appropriate. Fill in ExpectimaxAgent, where your agent 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 RandomGhost ghosts, which choose amongst their getLegalActions uniformly at random. You can debug your implementation on small game trees using the command:

python autograder.py -q q4

Once your algorithm is working on small trees, you can observe its success in Pacman. 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

Question 5 (5 points) 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. The autograder provided to you with the assignment tests your evaluation function on smallClassic with 1 ghost 10 times and assigns points (out of 6 possible points) as follows:

• If you win at least once without timing out the autograder, you receive 1 point.
• +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 additional points for average score and computation time are only awarded if you win at least 5 times.

Try it out with

python autograder.py -q q5

Grading: I will run your agent on the smallClassic layout with two ghosts 10 times. I 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 point. Any agent not satisfying this criterion will receive 0 points.
• +1 for winning at least 5 times or +2 for winning 10 times.
• +1 for an average winning score of at least 800, +2 for an average winning score of at least 1200
• The additional points for average score 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 reciprocals 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.

Mini Contest (3 points extra credit) Pacman's been doing well so far, but things are about to get a bit more challenging. This time, Pacman will be pitted against smarter foes in a trickier maze. In particular, the ghosts will actively chase Pacman instead of wandering around randomly, and the maze features more twists and dead-ends, but also extra pellets to give Pacman a fighting chance. You're free to have Pacman use any search procedure, search depth, and evaluation function you like. The only limit is that games can last a maximum of 3 minutes (with graphics off), so be sure to use your computation wisely. I'll run the contest with the following command:

python pacman.py -l contestClassic -p ContestAgent -g DirectionalGhost -q -n 5

Provided your individual games never take longer than 3 minutes, I'll discard the highest and lowest scores and then average the remaining three scores. The two teams with the highest scores will receive 3 and 2 extra credit points respectively and can look on with pride as their Pacman agents are shown off in class.

Project 2 is done. Go Pacman!