Pac-Man, now with ghosts.
In this project, you will design agents for the classic version of Pac-Man, 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. You can, however, use your
searchAgents.py in any way you want.
The code for this project contains the following files, available as a zip archive.
||Where all of your multi-agent search agents will reside.|
|The main file that runs Pac-Man games. This file also describes a Pac-Man |
||The logic behind how the Pac-Man world works. This file describes several supporting types like AgentState, Agent, Direction, and Grid.|
||Useful data structures for implementing search algorithms.|
||Graphics for Pac-Man|
||Support for Pac-Man graphics|
||ASCII graphics for Pac-Man|
||Agents to control ghosts|
||Keyboard interfaces to control Pac-Man|
||Code for reading layout files and storing their contents|
What to submit: You will fill in portions of
during the assignment. You should submit this file with your code and comments. You may 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 our original files other than
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.
Getting Help: You are not alone! If you find yourself stuck on something, contact the course staff for help. Office hours are there for your support; please use them. You are also welcome to contact us via email.
First, play a game of classic Pac-Man:
python pacman.pyNow, run the provided
python pacman.py -p ReflexAgentNote that it plays quite poorly even on simple layouts:
python pacman.py -p ReflexAgent -l testClassicInspect its code (in
multiAgents.py) and make sure you understand what it's doing.
Question 1 (3 points) Improve the
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
python pacman.py -p ReflexAgent -l testClassicTry out your reflex agent on the default
mediumClassiclayout 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 2How does your agent fare? It will likely often die with 2 ghosts on the default board, unless your evaluation function is quite good.
Note: you can never have more ghosts than the layout permits.
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.
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.
The autograder will check that your agent can rapidly clear the
openClassic layout ten times without dying more than twice or thrashing around infinitely (i.e. repeatedly moving back and forth between two positions, making no progress).
python pacman.py -p ReflexAgent -l openClassic -n 10 -q
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 a fix depth, which will be specified at the command line. Score the leaves of your minimax tree with the supplied
self.evaluationFunction, which defaults to
MultiAgentAgent, which gives access to
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 Pac-Man move and all the ghosts' responses, so depth 2 search will involve Pac-Man and each ghost moving two times.
Hints and Observations
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.
minimaxClassiclayout 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
Directions.STOPaction from Pac-Man's list of possible actions. Depth 2 should be pretty quick, but depth 3 or 4 will be slow. Don't worry, the next question will speed up the search somewhat.
GameStates, either passed in to
getActionor generated via
GameState.generateSuccessor. In this project, you will not be abstracting to simplified states.
mediumClassic(the default), you'll find Pac-Man 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.
python pacman.py -p MinimaxAgent -l trappedClassic -a depth=3Make sure you understand why Pac-Man rushes the closest ghost in this case.
Question 3 (3 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). 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
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.
Question 4 (3 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
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 should now observe a more cavalier approach in close quarters with ghosts. In particular, if Pac-Man 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 10You should find that your
ExpectimaxAgentwins about half the time, while your
AlphaBetaAgentalways loses. Make sure you understand why the behavior here differs from the minimax case.
Question 5 (6 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 two random ghosts more than half the time and still run at a reasonable rate (to get full credit, Pac-Man should be averaging around 1000 points when he's winning).
python pacman.py -l smallClassic -p ExpectimaxAgent -a evalFn=better -q -n 10
Document your evaluation function! We're very curious about what great ideas you have, so don't be shy. We reserve the right to reward bonus points for clever solutions and show demonstrations in class.
Hints and Observations
Mini Contest (3 points extra credit) Pac-Man's been doing well so far, but things are about to get a bit more challenging. This time, we'll pit Pac-Man against smarter foes in a trickier maze. In particular, the ghosts will actively chase Pac-Man instead of wandering around randomly, and the maze features more twists and dead-ends, but also extra pellets to give Pac-Man a fighting chance. You're free to have Pac-Man 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. We'll run the contest with the following command:
python pacman.py -l contestClassic -p ContestAgent -g DirectionalGhost -q -n 10
The three students with the highest score (details: we run 10 games; games longer than 3 minutes get score 0; lowest and highest 2 scores discarded; the remaining 6 scores averaged) will receive up to 3, 2 extra-credit points depending on performance. Be sure to document what your agent is doing, as we may award additional extra credit to creative solutions even if they're not in the top 3. We may also demonstrate the performance of winning or creative solutions in class.
Project 2 is done. Go Pac-Man!