# inference.py # ------------ # Licensing Information: You are free to use or extend these projects for # educational purposes provided that (1) you do not distribute or publish # solutions, (2) you retain this notice, and (3) you provide clear # attribution to UC Berkeley, including a link to http://ai.berkeley.edu. # # Attribution Information: The Pacman AI projects were developed at UC Berkeley. # The core projects and autograders were primarily created by John DeNero # (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu). # Student side autograding was added by Brad Miller, Nick Hay, and # Pieter Abbeel (pabbeel@cs.berkeley.edu). import itertools import util import random import busters import game class InferenceModule: """ An inference module tracks a belief distribution over a ghost's location. This is an abstract class, which you should not modify. """ ############################################ # Useful methods for all inference modules # ############################################ def __init__(self, ghostAgent): "Sets the ghost agent for later access" self.ghostAgent = ghostAgent self.index = ghostAgent.index self.obs = [] # most recent observation position def getJailPosition(self): return (2 * self.ghostAgent.index - 1, 1) def getPositionDistribution(self, gameState): """ Returns a distribution over successor positions of the ghost from the given gameState. You must first place the ghost in the gameState, using setGhostPosition below. """ ghostPosition = gameState.getGhostPosition(self.index) # The position you set actionDist = self.ghostAgent.getDistribution(gameState) dist = util.Counter() for action, prob in actionDist.items(): successorPosition = game.Actions.getSuccessor(ghostPosition, action) dist[successorPosition] = prob return dist def setGhostPosition(self, gameState, ghostPosition): """ Sets the position of the ghost for this inference module to the specified position in the supplied gameState. Note that calling setGhostPosition does not change the position of the ghost in the GameState object used for tracking the true progression of the game. The code in inference.py only ever receives a deep copy of the GameState object which is responsible for maintaining game state, not a reference to the original object. Note also that the ghost distance observations are stored at the time the GameState object is created, so changing the position of the ghost will not affect the functioning of observeState. """ conf = game.Configuration(ghostPosition, game.Directions.STOP) gameState.data.agentStates[self.index] = game.AgentState(conf, False) return gameState def observeState(self, gameState): "Collects the relevant noisy distance observation and pass it along." distances = gameState.getNoisyGhostDistances() if len(distances) >= self.index: # Check for missing observations obs = distances[self.index - 1] self.obs = obs self.observe(obs, gameState) def initialize(self, gameState): "Initializes beliefs to a uniform distribution over all positions." # The legal positions do not include the ghost prison cells in the bottom left. self.legalPositions = [p for p in gameState.getWalls().asList(False) if p[1] > 1] self.initializeUniformly(gameState) ###################################### # Methods that need to be overridden # ###################################### def initializeUniformly(self, gameState): "Sets the belief state to a uniform prior belief over all positions." pass def observe(self, observation, gameState): "Updates beliefs based on the given distance observation and gameState." pass def elapseTime(self, gameState): "Updates beliefs for a time step elapsing from a gameState." pass def getBeliefDistribution(self): """ Returns the agent's current belief state, a distribution over ghost locations conditioned on all evidence so far. """ pass class ExactInference(InferenceModule): """ The exact dynamic inference module should use forward-algorithm updates to compute the exact belief function at each time step. """ def initializeUniformly(self, gameState): "Begin with a uniform distribution over ghost positions." self.beliefs = util.Counter() for p in self.legalPositions: self.beliefs[p] = 1.0 self.beliefs.normalize() def observe(self, observation, gameState): """ Updates beliefs based on the distance observation and Pacman's position. The noisyDistance is the estimated Manhattan distance to the ghost you are tracking. The emissionModel below stores the probability of the noisyDistance for any true distance you supply. That is, it stores P(noisyDistance | TrueDistance). self.legalPositions is a list of the possible ghost positions (you should only consider positions that are in self.legalPositions). A correct implementation will handle the following special case: * When a ghost is captured by Pacman, all beliefs should be updated so that the ghost appears in its prison cell, position self.getJailPosition() You can check if a ghost has been captured by Pacman by checking if it has a noisyDistance of None (a noisy distance of None will be returned if, and only if, the ghost is captured). """ noisyDistance = observation emissionModel = busters.getObservationDistribution(noisyDistance) pacmanPosition = gameState.getPacmanPosition() "*** YOUR CODE HERE ***" util.raiseNotDefined() # Replace this code with a correct observation update # Be sure to handle the "jail" edge case where the ghost is eaten # and noisyDistance is None allPossible = util.Counter() for p in self.legalPositions: trueDistance = util.manhattanDistance(p, pacmanPosition) if emissionModel[trueDistance] > 0: allPossible[p] = 1.0 "*** END YOUR CODE HERE ***" allPossible.normalize() self.beliefs = allPossible def elapseTime(self, gameState): """ Update self.beliefs in response to a time step passing from the current state. The transition model is not entirely stationary: it may depend on Pacman's current position (e.g., for DirectionalGhost). However, this is not a problem, as Pacman's current position is known. In order to obtain the distribution over new positions for the ghost, given its previous position (oldPos) as well as Pacman's current position, use this line of code: newPosDist = self.getPositionDistribution(self.setGhostPosition(gameState, oldPos)) Note that you may need to replace "oldPos" with the correct name of the variable that you have used to refer to the previous ghost position for which you are computing this distribution. You will need to compute multiple position distributions for a single update. newPosDist is a util.Counter object, where for each position p in self.legalPositions, newPostDist[p] = Pr( ghost is at position p at time t + 1 | ghost is at position oldPos at time t ) (and also given Pacman's current position). You may also find it useful to loop over key, value pairs in newPosDist, like: for newPos, prob in newPosDist.items(): ... *** GORY DETAIL AHEAD *** As an implementation detail (with which you need not concern yourself), the line of code at the top of this comment block for obtaining newPosDist makes use of two helper methods provided in InferenceModule above: 1) self.setGhostPosition(gameState, ghostPosition) This method alters the gameState by placing the ghost we're tracking in a particular position. This altered gameState can be used to query what the ghost would do in this position. 2) self.getPositionDistribution(gameState) This method uses the ghost agent to determine what positions the ghost will move to from the provided gameState. The ghost must be placed in the gameState with a call to self.setGhostPosition above. It is worthwhile, however, to understand why these two helper methods are used and how they combine to give us a belief distribution over new positions after a time update from a particular position. """ "*** YOUR CODE HERE ***" util.raiseNotDefined() def getBeliefDistribution(self): return self.beliefs class ParticleFilter(InferenceModule): """ A particle filter for approximately tracking a single ghost. Useful helper functions will include random.choice, which chooses an element from a list uniformly at random, and util.sample, which samples a key from a Counter by treating its values as probabilities. """ def __init__(self, ghostAgent, numParticles=300): InferenceModule.__init__(self, ghostAgent); self.setNumParticles(numParticles) def setNumParticles(self, numParticles): self.numParticles = numParticles def initializeUniformly(self, gameState): """ Initializes a list of particles. Use self.numParticles for the number of particles. Use self.legalPositions for the legal board positions where a particle could be located. Particles should be evenly (not randomly) distributed across positions in order to ensure a uniform prior. Note: the variable you store your particles in must be a list; a list is simply a collection of unweighted variables (positions in this case). Storing your particles as a Counter (where there could be an associated weight with each position) is incorrect and may produce errors. """ "*** YOUR CODE HERE ***" def observe(self, observation, gameState): """ Update beliefs based on the given distance observation. Make sure to handle the special case where all particles have weight 0 after reweighting based on observation. If this happens, resample particles uniformly at random from the set of legal positions (self.legalPositions). A correct implementation will handle two special cases: 1) When a ghost is captured by Pacman, all particles should be updated so that the ghost appears in its prison cell, self.getJailPosition() As before, you can check if a ghost has been captured by Pacman by checking if it has a noisyDistance of None. 2) When all particles receive 0 weight, they should be recreated from the prior distribution by calling initializeUniformly. The total weight for a belief distribution can be found by calling totalCount on a Counter object util.sample(Counter object) is a helper method to generate a sample from a belief distribution. You may also want to use util.manhattanDistance to calculate the distance between a particle and Pacman's position. """ noisyDistance = observation emissionModel = busters.getObservationDistribution(noisyDistance) pacmanPosition = gameState.getPacmanPosition() "*** YOUR CODE HERE ***" util.raiseNotDefined() def elapseTime(self, gameState): """ Update beliefs for a time step elapsing. As in the elapseTime method of ExactInference, you should use: newPosDist = self.getPositionDistribution(self.setGhostPosition(gameState, oldPos)) to obtain the distribution over new positions for the ghost, given its previous position (oldPos) as well as Pacman's current position. util.sample(Counter object) is a helper method to generate a sample from a belief distribution. """ "*** YOUR CODE HERE ***" util.raiseNotDefined() def getBeliefDistribution(self): """ Return the agent's current belief state, a distribution over ghost locations conditioned on all evidence and time passage. This method essentially converts a list of particles into a belief distribution (a Counter object) """ "*** YOUR CODE HERE ***" util.raiseNotDefined() class MarginalInference(InferenceModule): """ A wrapper around the JointInference module that returns marginal beliefs about ghosts. """ def initializeUniformly(self, gameState): "Set the belief state to an initial, prior value." if self.index == 1: jointInference.initialize(gameState, self.legalPositions) jointInference.addGhostAgent(self.ghostAgent) def observeState(self, gameState): "Update beliefs based on the given distance observation and gameState." if self.index == 1: jointInference.observeState(gameState) def elapseTime(self, gameState): "Update beliefs for a time step elapsing from a gameState." if self.index == 1: jointInference.elapseTime(gameState) def getBeliefDistribution(self): "Returns the marginal belief over a particular ghost by summing out the others." jointDistribution = jointInference.getBeliefDistribution() dist = util.Counter() for t, prob in jointDistribution.items(): dist[t[self.index - 1]] += prob return dist class JointParticleFilter: """ JointParticleFilter tracks a joint distribution over tuples of all ghost positions. """ def __init__(self, numParticles=600): self.setNumParticles(numParticles) def setNumParticles(self, numParticles): self.numParticles = numParticles def initialize(self, gameState, legalPositions): "Stores information about the game, then initializes particles." self.numGhosts = gameState.getNumAgents() - 1 self.ghostAgents = [] self.legalPositions = legalPositions self.initializeParticles() def initializeParticles(self): """ Initialize particles to be consistent with a uniform prior. Each particle is a tuple of ghost positions. Use self.numParticles for the number of particles. You may find the `itertools` package helpful. Specifically, you will need to think about permutations of legal ghost positions, with the additional understanding that ghosts may occupy the same space. Look at the `itertools.product` function to get an implementation of the Cartesian product. Note: If you use itertools, keep in mind that permutations are not returned in a random order; you must shuffle the list of permutations in order to ensure even placement of particles across the board. Use self.legalPositions to obtain a list of positions a ghost may occupy. Note: the variable you store your particles in must be a list; a list is simply a collection of unweighted variables (positions in this case). Storing your particles as a Counter (where there could be an associated weight with each position) is incorrect and may produce errors. """ "*** YOUR CODE HERE ***" def addGhostAgent(self, agent): """ Each ghost agent is registered separately and stored (in case they are different). """ self.ghostAgents.append(agent) def getJailPosition(self, i): return (2 * i + 1, 1); def observeState(self, gameState): """ Resamples the set of particles using the likelihood of the noisy observations. To loop over the ghosts, use: for i in range(self.numGhosts): ... A correct implementation will handle two special cases: 1) When a ghost is captured by Pacman, all particles should be updated so that the ghost appears in its prison cell, position self.getJailPosition(i) where `i` is the index of the ghost. As before, you can check if a ghost has been captured by Pacman by checking if it has a noisyDistance of None. 2) When all particles receive 0 weight, they should be recreated from the prior distribution by calling initializeParticles. After all particles are generated randomly, any ghosts that are eaten (have noisyDistance of None) must be changed to the jail Position. This will involve changing each particle if a ghost has been eaten. self.getParticleWithGhostInJail is a helper method to edit a specific particle. Since we store particles as tuples, they must be converted to a list, edited, and then converted back to a tuple. This is a common operation when placing a ghost in jail. """ pacmanPosition = gameState.getPacmanPosition() noisyDistances = gameState.getNoisyGhostDistances() if len(noisyDistances) < self.numGhosts: return emissionModels = [busters.getObservationDistribution(dist) for dist in noisyDistances] "*** YOUR CODE HERE ***" def getParticleWithGhostInJail(self, particle, ghostIndex): """ Takes a particle (as a tuple of ghost positions) and returns a particle with the ghostIndex'th ghost in jail. """ particle = list(particle) particle[ghostIndex] = self.getJailPosition(ghostIndex) return tuple(particle) def elapseTime(self, gameState): """ Samples each particle's next state based on its current state and the gameState. To loop over the ghosts, use: for i in range(self.numGhosts): ... Then, assuming that `i` refers to the index of the ghost, to obtain the distributions over new positions for that single ghost, given the list (prevGhostPositions) of previous positions of ALL of the ghosts, use this line of code: newPosDist = getPositionDistributionForGhost( setGhostPositions(gameState, prevGhostPositions), i, self.ghostAgents[i] ) Note that you may need to replace `prevGhostPositions` with the correct name of the variable that you have used to refer to the list of the previous positions of all of the ghosts, and you may need to replace `i` with the variable you have used to refer to the index of the ghost for which you are computing the new position distribution. As an implementation detail (with which you need not concern yourself), the line of code above for obtaining newPosDist makes use of two helper functions defined below in this file: 1) setGhostPositions(gameState, ghostPositions) This method alters the gameState by placing the ghosts in the supplied positions. 2) getPositionDistributionForGhost(gameState, ghostIndex, agent) This method uses the supplied ghost agent to determine what positions a ghost (ghostIndex) controlled by a particular agent (ghostAgent) will move to in the supplied gameState. All ghosts must first be placed in the gameState using setGhostPositions above. The ghost agent you are meant to supply is self.ghostAgents[ghostIndex-1], but in this project all ghost agents are always the same. """ newParticles = [] for oldParticle in self.particles: newParticle = list(oldParticle) # A list of ghost positions # now loop through and update each entry in newParticle... "*** YOUR CODE HERE ***" "*** END YOUR CODE HERE ***" newParticles.append(tuple(newParticle)) self.particles = newParticles def getBeliefDistribution(self): "*** YOUR CODE HERE ***" util.raiseNotDefined() # One JointInference module is shared globally across instances of MarginalInference jointInference = JointParticleFilter() def getPositionDistributionForGhost(gameState, ghostIndex, agent): """ Returns the distribution over positions for a ghost, using the supplied gameState. """ # index 0 is pacman, but the students think that index 0 is the first ghost. ghostPosition = gameState.getGhostPosition(ghostIndex+1) actionDist = agent.getDistribution(gameState) dist = util.Counter() for action, prob in actionDist.items(): successorPosition = game.Actions.getSuccessor(ghostPosition, action) dist[successorPosition] = prob return dist def setGhostPositions(gameState, ghostPositions): "Sets the position of all ghosts to the values in ghostPositionTuple." for index, pos in enumerate(ghostPositions): conf = game.Configuration(pos, game.Directions.STOP) gameState.data.agentStates[index + 1] = game.AgentState(conf, False) return gameState