Description

Hwanjo Yu
CSED342 – Artificial Intelligence
General Instructions
This (and every) assignment has a written part and a programming part.
You should write both types of answers in submission.py between
# BEGIN_YOUR_ANSWER and
# END_YOUR_ANSWER
ÒThis icon means a written answer is expected. Some of these problems are multiple choice questions that impose negative scores if the answers are incorrect. So, don’t write answers unless you are confident.
¥This icon means you should write code. you can add other helper functions outside the answer block if you want. Do not make changes to files other than submission.py.
Your code will be evaluated on two types of test cases, basic and hidden, which you can see in grader.py. Basic tests, which are fully provided to you, do not stress your code with large inputs or tricky corner cases. Hidden tests are more complex and do stress your code. The inputs of hidden tests are provided in grader.py, but the correct outputs are not. To run all the tests, type
python grader.py
This will tell you only whether you passed the basic tests. On the hidden tests, the script will alert you if your code takes too long or crashes, but does not say whether you got the correct output. You can also run a single test (e.g., 3a-0-basic) by typing
python grader.py 3a-0-basic
We strongly encourage you to read and understand the test cases, create your own test cases, and not just blindly run grader.py.
Introduction

Figure 1: Pac-Man, now with ghosts.
For those of you not familiar with Pac-Man, it’s a game where Pac-Man (the yellow circle with a mouth in the above figure) moves around in a maze and tries to eat as many food pellets (the small white dots) as possible, while avoiding the ghosts (the other two agents with eyes in the above figure). If Pac-Man eats all the food in a maze, it wins. The big white dots at the top-left and bottom-right corner are capsules, which give Pac-Man power to eat ghosts in a limited time window (but you won’t be worrying about them for the required part of the assignment). You can get familiar with the setting by playing a few games of classic Pac-Man, which we come to just after this introduction.
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.
Files
• submission.py : Where all of your multi-agent search agents will reside and the only file you need to concern yourself with for this assignment.
• pacman.py : The main file that runs Pac-Man games. This file also describes a Pac-Man GameState type, which you will use extensively in this project
• game.py : The logic behind how the Pac-Man world works. This file describes several supporting types like AgentState, Agent, Direction, and Grid.
• util.py : Useful data structures for implementing search algorithms.
• graphicsDisplay.py : Graphics for Pac-Man
• graphicsUtils.py : Support for Pac-Man graphics
• textDisplay.py : ASCII graphics for Pac-Man
• ghostAgents.py : Agents to control ghosts
• keyboardAgents.py : Keyboard interfaces to control Pac-Man
• layout.py : Code for reading layout files and storing their contents
Warmup
First, play a game of classic Pac-Man to get a feel for the assignment:
python pacman.py
You can always add –frameTime 1 to the command line to run in ”demo mode” where the game pauses after every frame.
Now, run the provided ReflexAgent in submission.py: python pacman.py -p ReflexAgent
Note that it plays quite poorly even on simple layouts: python pacman.py -p ReflexAgent -l testClassic
You can also try out the reflex agent on the default mediumClassic layout with one ghost or two.
python pacman.py -p ReflexAgent -k 1 python pacman.py -p ReflexAgent -k 2
Note: you can never have more ghosts than the layout permits.
Options: Default ghosts are random; you can also play for fun with slightly smarter directional ghosts using -g DirectionalGhost. You can also play multiple games in a row with -n. Turn off graphics with -q to run lots of games quickly.
So, now that you are familiar enough with the interface, inspect the ReflexAgent code carefully (in submission.py) and make sure you understand what it’s doing. The reflex agent code provides some helpful examples of methods that query the GameState (a GameState specifies the full game state, including the food, capsules, agent configurations and score changes: see submission.py for further information and helper methods) for information, which you will be using in the actual coding part. We are giving an exhaustive and very detailed description below, for the sake of completeness and to save you from digging deeper into the starter code. The actual coding part is very small – so please be patient if you think there is too much writing.
Note: if you wish to run Pac-Man in the terminal using a text-based interface, check out the terminal directory.
Problems
Problem 1: Minimax
Before you code up Pac-Man as a minimax agent, notice that instead of just one adversary, Pac-Man could have multiple ghosts as adversaries. So we will extend the minimax algorithm from class (which had only one min stage for a single adversary) to the more general case of multiple adversaries. In particular, your minimax tree will have multiple min layers (one for each ghost) for every max layer.
Specifically, consider the limited depth tree minimax search with evaluation functions taught in class. Suppose there are n + 1 agents on the board, a0,…,an, where a0 is PacMan and the rest are ghosts. Pac-Man acts as a max agent, and the ghosts act as min agents. A single depth consists of all n + 1 agents making a move, so depth 2 search will involve Pac-Man and each ghost moving two times. In other words, a depth of 2 corresponds to a height of 2(n + 1) in the minimax game tree.
First, design the recurrence for Vmax,min(s,d) in math. You should express the idea in terms of the following functions: IsEnd(s), which tells you if s is an end state; Utility(s), the utility of a state; Eval(s), an evaluation function for the state s; Player(s), which returns the player whose turn it is; Actions(s), which returns the possible actions; and Succ(s,a), which returns the successor state resulting from taking an action at a certain state. It would be helpful to review the recurrence of depth-limited search in lecture notes.
Problem 1a [6 points] ¥
Now fill out MinimaxAgent class in submission.py using the recurrence you designed. Remember that your minimax agent should work with any number of ghosts, and your minimax tree should 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. The class 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 from the command line options.
Other functions that you might use in the code: GameState.getLegalActions() which returns all the possible legal moves, where each move is Directions.X for some X in the set NORTH, SOUTH, WEST, EAST, STOP. Go through ReflexAgent code as suggested before to see how the above are used and also for other important methods like GameState.getPacmanState(), GameState.getGhostStates(), GameState.getScore() etc. These are further documented inside the MinimaxAgent class.
Hints and Observations
• The evaluation function 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. Use self.evaluationFunction in your definition of Vmax,min wherever you used Eval(s) in part 1a.
• The minimax values of the initial state in the minimaxClassic layout are 9, 8, 7, -492 for depths 1, 2, 3 and 4 respectively. You can use these numbers to verify if your implementation is correct. Note that your minimax agent will often win (just under 50% of the time for us–be sure to test on a large number of games using the -n and -q flags) despite the dire prediction of depth 4 minimax.
python pacman.py -p MinimaxAgent -l minimaxClassic -a depth=4 • Pac-Man is always agent 0, and the agents move in order of increasing agent index. Use self.index in your minimax implementation, but only Pac-Man will actually be running your MinimaxAgent.
• Functions are provided to get legal moves for Pac-Man or the ghosts and to execute a move by any agent. See GameState in pacman.py for details.
• 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.
• getAction should use Vmax,min to determine the best action for Pac-Man.
• On larger boards such as openClassic and 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. Don’t worry if you see this behavior.
• Consider the following run: python pacman.py -p MinimaxAgent -l trappedClassic -a depth=3
Why do you think Pac-Man rushes the closest ghost in minimax search on trappedClassic? • You can assume that you will always have at least one action from which to choose in getAction.
Problem 2: Alpha-beta pruning
Problem 2a [6 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 slides, 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 mediumClassic should run in just a few seconds per move or faster. python pacman.py -p AlphaBetaAgent -a depth=3
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. Running the command given above this paragraph, the minimax values of the initial state should be 9, 18, 27, and 36 for depths 1, 2, 3, and 4, respectively.
Problem 3: Expectimax
Random ghosts are of course not optimal minimax agents, so modeling them with minimax search is not optimal. Let’s assume that ghosts follow the uniform policy, therefore ghosts take legal actions uniformly in any state. Before implementing it, first extend Expectimax recurrence, so the algorithm considers multiple ghosts as opponents.Your recurrence should resemble that of Problem 1a
Problem 3a [6 points] ¥
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. Assume Pac-Man is playing against RandomGhosts, which each choose getLegalActions uniformly at random.
You should now observe a more cavalier approach to 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:
python pacman.py -p ExpectimaxAgent -l trappedClassic -a depth=3
Problem 4: Evaluation function (extra credit)
Problem 4a [5 points] ¥
python pacman.py -l smallClassic -p ExpectimaxAgent -a evalFn=better -q -n 20
We will run your Pac-Man agent 20 times, and calculate the average score you obtained. If your average score is less than 700, you’ll get no point. If your average score is more than 1500, you’ll get 5 points. Check the grader.py to see how the scores are calculated.
Hints and Observations
• Having gone through the rest of the assignment, you should play Pac-Man again yourself and think about what kinds of features you want to add to the evaluation function. How can you add multiple features to your evaluation function?
• For your information, our solution code gets more than 1600 scores in average with various random seeds.