Assignment #2: Search solution

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 les 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:




python2 autograder.py




It can be run for one particular question, such as q2, by:




python2 autograder.py -q q2




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 ag, or force no graphics by using the --no-graphics ag.




See the autograder tutorial in Assignment 0 for more information about using the autograder.




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




Files you'll edit:




multiAgents.py Where all of your multi-agent search agents will reside.




Files you can ignore:




pacman.py The main le that runs Pacman games.




This le 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 le describes several supporting types like AgentState, Agent, Direction, and Grid.




util.py Useful data structures for implementing search algorithms.




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 les and storing their contents




autograder.py Assignment autograder




testParser.py Parses autograder test and solution les




testClasses.py General autograding test classes

test_cases/ Directory containing some test cases for each question




multiagentTestClasses.py Assignment 2 speci c autograding test classes




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Files to Edit and Submit: You will ll in portions of multiAgents.py during the assignment. You may also add other functions and code to this le so as to create a modular implementation. You will submit this le with your modi cations. Please do not change the other les in this distribution or submit any of our original les other than this le.




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. We will also run some additional tests on your code, in addition to tests supplied in the zip le. If all checks out with your code you will receive all of the points indicated by the autograder, and some more for the additional tests.




Getting Help: You are not alone! If you nd yourself stuck on something, contact us for help. The piazza discussion forum will be monitored and questions answered, and you can also ask questions about the assignment during o ce hours. If you can't make our o ce hours, let us know and we will arrange a di erent appointment. We want the assignment to be rewarding and instructional, not frustrating and demoralizing. But, we don't know when or how to help unless you ask.




Piazza Discussion: Please be careful not to post spoilers.







What to Submit




You will be using MarkUs to submit your assignment. MarkUs accounts for the course will be soon be set up. You will submit three les:




Your modi ed multiAgents.py




A signed copy of the following acknowledgment




Note: In the various parts below we ask a number of questions. You do not have to hand in answers to these questions, rather these questions are designed to help you understand what is going on with search.







Multi-Agent Pacman




First, play a game of classic Pacman:




python2 pacman.py




Now, run the provided ReflexAgent in multiAgents.py:




python2 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): Re ex Agent




Don't spend too much time on this question, as the meat of the project lies ahead.




Improve the ReflexAgent in multiAgents.py to play respectably. The provided re ex agent code provides some helpful examples of methods that query the GameState for information. A capable re ex 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 re ex agent on the default mediumClassic layout with one ghost or two (and animation o to speed up the display):










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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 food) rather than just the values themselves.




Note: The evaluation function you're writing is evaluating state-action pairs (i.e., how good is it to perform this action in this state); in later parts of the project, you'll be evaluating states (i.e., how good is it to be in this state).




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 xed random seed (same random choices every game). You can also play multiple games in a row with -n. Turn o 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







Question 2 (5 points): Minimax




Now you will write an adversarial search agent in the provided MinimaxAgent class stub in multiAgents.py. Your minimax search must work with any number of ghosts. In particular, for every max layer (where the pacman moves) your minimax tree will have multiple min layers, one for each ghost.




gameState does not keep track of whose turn it is to play, you will have to keep track of that in your minimax followed by each ghost getting a turn; then the pacman plays again, followed by each ghost getting a turn, etc.




Score the leaves of your minimax tree with the supplied self.evaluationFunction, which defaults to scoreEvaluationFunction. You will have to implement a depth-bound, so the leaves of your minimax tree could be either terminal or non-terminal nodes. Hence, self.evaluationFunction will act as the game utility function, except that it will be called both on terminal and non-terminal nodes.




Terminal nodes are nodes where either gameState.isWin() or gameState.isLose() is true. However, the leaves of your tree search might also be non-terminal nodes.




Your Minimax (and all other game tree search algorithms you will implement) must utilize a depth-bound. The depth-bound you must operate under is stored in the variable self.depth. The depth-bound speci es number of times the pacman (MAX) gets to play. For example, if the depth-bound is 2, then MAX gets to make 2 moves and all of the ghosts get 2 moves each. When MAX is about to play a 3rd time, your search will terminate: instead of considering the possible 3rd moves of MAX it will simply return the value of self.evaluationFunction treating this node as if it was a terminal node. As another example, if the depth-bound is zero, your search will immediately return the self.evaluationFunction value of the root node.




Make sure your minimax code makes reference to the two variables, self.depth and self.evaluationFunction where appropriate as these variables will vary in response to command line options.




Grading: We 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.generateSuccessor.







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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 ac-tions, as we were for the re ex agent. Look-ahead agents evaluate future states whereas re ex 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 simpli ed states.




On larger boards such as openClassic and mediumClassic (the default), you'll nd 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): Alpha-Beta Pruning




Make a new agent that uses alpha-beta pruning to more e ciently explore the minimax tree, in AlphaBetaAgent. Again, your algorithm must use the depth-bound speci ed in self.depth and evaluate its leaf nodes with self.evaluationFunction.




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. 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.







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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.




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 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 nd bugs quickly. Make sure when you compute your averages that you use oats. Integer division in Python truncates, so that 1/2 = 0, unlike the case with oats where 1.0/2.0 = 0.5.




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. 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 nd that your ExpectimaxAgent wins about half the time, while your AlphaBetaAgent always loses. Make sure you understand why the behavior here di ers 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.







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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 re ex 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).




python autograder.py -q q5




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 1000 (including scores on lost games)




+1 if your games take on average less than 30 seconds on the autograder machine. The autograder is run on the cslinux machine which has a fair amount of resources, but your personal computer could be far less performant (netbooks) or far more performant (gaming rigs). You can use your cslinux login to run your program on the school machines.




The additional points for average score and computation time will only be awarded if you win at least 5 times.




Hints and Observations




As for your re ex agent evaluation function, you may want to use the reciprocal 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 di erent values and adding the results together. You might decide what to multiply each feature by based on how important you think it is.







Academic Honesty




We are aware that solutions to the original Berkeley project exist on the internet. Do not use these solutions as this would be plagiarism. To earn marks on this assignment you must develop your own solutions. Also please consider the following points.




You are to implement the search algorithms presented in the course. These algorithms di er in subtle but important ways from other presentations of this material. If you implement your search based on other non-course material it might give the wrong answers. If you try to use solutions found on the internet the same problem might occur.




We will check for answers that would arise from solutions to the original Berkeley project. Such answers indicate that your solution is incorrect, reproducing the errors of the Berkeley lectures. This will cause you to fail some of our additional tests and you will lose marks for those tests.







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If we nd evidence of plagiarism we will investigate thoroughly and we will send your case to the University Academic O enses O ce.




Please do not implement your own "improvement" to the search algorithms: it will wreak havoc with the automarker. (Note, if you have invented a signi cant improvement we would be happy to hear about it, but don't use it in this assignment).




You will be asked to write, sign, scan, and submit a statement acknowledging that the code you submitted was written by you.




Although the assignment includes an autograder, additional tests will be run on your code after sub-mission.







Working successfully in a pair




You may work in pairs for this assignment.




If you are working with a partner, make sure that you are actually working together. Your goal should be for the two of you to help each other learn the material and to avoid getting stuck with frustrating errors. If you split up the assignment and work separately, you are not getting practice on all aspects of the assignment.




Sometimes a student who is working with a partner drops the course or becomes ill in the middle of an assignment. If this happens, the other partner is still responsible for completing the assignment on time. If he or she has been actively engaged in the entire assignment, this should not be a problem; the assignments are designed so that an individual student can complete them. However, if the remaining partner has not been actively involved or does not have copies of all of the work, they will have serious di culty completing the assignment. Make sure you don't nd yourself in this situation: Be active in all parts of the assignment, and make sure that at the end of each meeting, both partners have a copy of all of the work.