Project 3 - Pacman with Ghosts

In this project, you will design agents for the classic version of Pacman. The basis for this game and the course code for the game itself were developed by Berkerly AI (http://ai.berkeley.edu). The code base has not changed much from the previous project, but please start with a fresh installation, rather than intermingling files from PA 1.

As in PA 1, this project includes an autograder for you to grade your answers on your machine.

Tasks

1. Download pacmanMultiagent.zip file and unzip it in a directory.

2. Complete the programming tasks below (questions 1 - 3).

3. Submit your assignment to Gradescope.

NOTE You do not need to complete the betterEvaluationFunction at this time (it is NOT part of this PA).

Question 1 Minimax

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 each 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 and respects 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’ getting a single move. So, a depth 2 search gives Pacman and each ghost two moves each. While this seems to differ from the definition of ply given in the reading, the fact that Pacman and the ghosts each move in one time step hopefully clarifies why this is considered a single ply.

Grading: Your code will be checked 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 q1

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 q1 --no-graphics

Hints and Observations

1. Implement the algorithm recursively using helper function(s).
2. 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.
3. 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.
4. 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

1. Pacman is always agent 0, and the agents move in order of increasing agent index.

2. 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.

3. 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.

4. 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 2 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 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 the 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.

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

Question 3 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 algorithms 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 the small game trees using the command:

python autograder.py -q q3

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. Rather than taking the min over all ghost actions, the ExpectimaxAgent will take 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 that chooses among its 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 AlphaBetaAgent -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 behavior, it will pass the tests.

Submission and Grading

You should never start design or construction until you completely understand the project.

You should start by carefully reading the project specifications. (In general it is a good idea to print a paper copy so that you can take notes and perform calculations as you read.)

Implement all of the classes (in accordance with the specifications, perhaps informed by the implementation hints above) and submit them to gradescope.

You are not required to submit test cases for these classes but it is strongly recommended to use the small test cases and in the event you need help, showcase one of these tests failing and where in the test you receive the unexpected/incorrect results.

Make sure that your code:

• contains comments that provide clarity
• has meaningful variable names
• Acknowledgements and honor code statement (as appropriate)

You may submit to Gradescope an unlimited number of times.