Project 4: Ghostbusters (Part II)

Table of contents

• Introduction
• Ghostbusters and Bayes Nets
• Question 1, 2, 3, 4
• Question 5a: DiscreteDistribution Class
• Question 5b (1 point): Observation Probability
• Question 6 (3 points): Exact Inference Observation
• Question 7 (3 points): Exact Inference with Time Elapse
• Question 8 (1 point): Exact Inference Full Test
• Question 9 (2 points): Approximate Inference Initialization and Beliefs
• Question 10 (3 points): Approximate Inference Observation
• Question 11 (3 points): Approximate Inference with Time Elapse
• Submission

Introduction

This project follows Project 3 Ghostbusters Part I.

The code for this project contains the following files. You can download all the code and supporting files from this GitHub repository.

Files to Edit and Submit: You will fill in portions of bustersAgents.py, inference.py, and factorOperations.py during the assignment. Once you have completed the assignment, you will submit a token generated by submission_autograder.py to Gradescope. The token contains these your code and the outputs generated by your code on some test cases. Please do not change the other files in this distribution.

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. If necessary, we will review and grade assignments individually to ensure that you receive due credit for your work.

Academic Dishonesty: We will be checking your code against other submissions in the class for logical redundancy. If you copy someone else’s code and submit it with minor changes, we will know. These cheat detectors are quite hard to fool, so please don’t try. We trust you all to submit your own work only; please don’t let us down. If you do, we will pursue the strongest consequences available to us.

Getting Help: You are not alone! If you find yourself stuck on something, contact the course staff for help. Office hours, section, and the discussion forum are there for your support; please use them. If you can’t make our office hours, let us know and we will schedule more. We want these projects to be rewarding and instructional, not frustrating and demoralizing. But, we don’t know when or how to help unless you ask.

Discussion: Please be careful not to post spoilers.

Ghostbusters and Bayes Nets

Question 1, 2, 3, 4

Use your Project 3 solution for questions Q1, Q2, Q3, and Q4. Autograder tests from Project 3 are included for reference, but they will not contribute to your Project 4 scores.

Question 5a: DiscreteDistribution Class

Unfortunately, having timesteps will grow our graph far too much for variable elimination to be viable. Instead, we will use the Forward Algorithm for HMM’s for exact inference, and Particle Filtering for even faster but approximate inference.

For the rest of the project, we will be using the DiscreteDistribution class defined in inference.py to model belief distributions and weight distributions. This class is an extension of the built-in Python dictionary class, where the keys are the different discrete elements of our distribution, and the corresponding values are proportional to the belief or weight that the distribution assigns that element. This question asks you to fill in the missing parts of this class, which will be crucial for later questions (even though this question itself is worth no points).

First, fill in the normalize method, which normalizes the values in the distribution to sum to one, but keeps the proportions of the values the same. Use the total method to find the sum of the values in the distribution. For an empty distribution or a distribution where all of the values are zero, do nothing. Note that this method modifies the distribution directly, rather than returning a new distribution.

Second, fill in the sample method, which draws a sample from the distribution, where the probability that a key is sampled is proportional to its corresponding value. Assume that the distribution is not empty, and not all of the values are zero. Note that the distribution does not necessarily have to be normalized prior to calling this method. You may find Python’s built-in random.random() function useful for this question.

Question 5b (1 point): Observation Probability

In this question, you will implement the getObservationProb method in the InferenceModule base class in inference.py. This method takes in an observation (which is a noisy reading of the distance to the ghost), Pacman’s position, the ghost’s position, and the position of the ghost’s jail, and returns the probability of the noisy distance reading given Pacman’s position and the ghost’s position. In other words, we want to return \(\Pr(\mathrm{noisyDistance} \mid \mathrm{pacmanPosition}, \mathrm{ghostPosition})\).

The distance sensor has a probability distribution over distance readings given the true distance from Pacman to the ghost. This distribution is modeled by the function busters.getObservationProbability(noisyDistance, trueDistance), which returns \(\Pr(\mathrm{noisyDistance} \mid \mathrm{trueDistance})\) and is provided for you. You should use this function to help you solve the problem, and use the provided manhattanDistance function to find the distance between Pacman’s location and the ghost’s location.

However, there is the special case of jail that we have to handle as well. Specifically, when we capture a ghost and send it to the jail location, our distance sensor deterministically returns None, and nothing else (observation = None if and only if ghost is in jail). One consequence of this is that if the ghost’s position is the jail position, then the observation is None with probability 1, and everything else with probability 0. Make sure you handle this special case in your implementation; we effectively have a different set of rules for whenever ghost is in jail, as well as whenever observation is None.

To test your code and run the autograder for this question:

python autograder.py -q q5

Question 6 (3 points): Exact Inference Observation

In this question, you will implement the observeUpdate method in ExactInference class of inference.py to correctly update the agent’s belief distribution over ghost positions given an observation from Pacman’s sensors. You are implementing the online belief update for observing new evidence. The observeUpdate method should, for this problem, update the belief at every position on the map after receiving a sensor reading. You should iterate your updates over the variable self.allPositions which includes all legal positions plus the special jail position. Beliefs represent the probability that the ghost is at a particular location, and are stored as a DiscreteDistribution object in a field called self.beliefs, which you should update.

Before typing any code, write down the equation of the inference problem you are trying to solve. You should use the function self.getObservationProb that you wrote in the last question, which returns the probability of an observation given Pacman’s position, a potential ghost position, and the jail position. You can obtain Pacman’s position using gameState.getPacmanPosition(), and the jail position using self.getJailPosition().

In the Pacman display, high posterior beliefs are represented by bright colors, while low beliefs are represented by dim colors. You should start with a large cloud of belief that shrinks over time as more evidence accumulates. As you watch the test cases, be sure that you understand how the squares converge to their final coloring.

Note: your busters agents have a separate inference module for each ghost they are tracking. That’s why if you print an observation inside the observeUpdate function, you’ll only see a single number even though there may be multiple ghosts on the board.

To run the autograder for this question and visualize the output:

python autograder.py -q q6

If you want to run this test (or any of the other tests) without graphics you can add the following flag:

python autograder.py -q q6 --no-graphics

Question 7 (3 points): Exact Inference with Time Elapse

In the previous question you implemented belief updates for Pacman based on his observations. Fortunately, Pacman’s observations are not his only source of knowledge about where a ghost may be. Pacman also has knowledge about the ways that a ghost may move; namely that the ghost can not move through a wall or more than one space in one time step.

To understand why this is useful to Pacman, consider the following scenario in which there is Pacman and one Ghost. Pacman receives many observations which indicate the ghost is very near, but then one which indicates the ghost is very far. The reading indicating the ghost is very far is likely to be the result of a buggy sensor. Pacman’s prior knowledge of how the ghost may move will decrease the impact of this reading since Pacman knows the ghost could not move so far in only one move.

In this question, you will implement the elapseTime method in ExactInference. The elapseTime step should, for this problem, update the belief at every position on the map after one time step elapsing. Your agent has access to the action distribution for the ghost through self.getPositionDistribution. In order to obtain the distribution over new positions for the ghost, given its previous position, use this line of code:

newPosDist = self.getPositionDistribution(gameState, oldPos)

Where oldPos refers to the previous ghost position. newPosDist is a DiscreteDistribution object, where for each position p in self.allPositions, newPosDist[p] is the probability that the ghost is at position p at time t + 1, given that the ghost is at position oldPos at time t. Note that this call can be fairly expensive, so if your code is timing out, one thing to think about is whether or not you can reduce the number of calls to self.getPositionDistribution.

Before typing any code, write down the equation of the inference problem you are trying to solve. In order to test your predict implementation separately from your update implementation in the previous question, this question will not make use of your update implementation.

Since Pacman is not observing the ghost’s actions, these actions will not impact Pacman’s beliefs. Over time, Pacman’s beliefs will come to reflect places on the board where he believes ghosts are most likely to be given the geometry of the board and ghosts’ possible legal moves, which Pacman already knows.

For the tests in this question we will sometimes use a ghost with random movements and other times we will use the GoSouthGhost. This ghost tends to move south so over time, and without any observations, Pacman’s belief distribution should begin to focus around the bottom of the board. To see which ghost is used for each test case you can look in the .test files.

The below diagram shows what the Bayes Net/ Hidden Markov model for what is happening. Still, you should rely on the above description for implementation because some parts are implemented for you (i.e. getPositionDistribution is abstracted to be \(\Pr(G_{t+1} \mid \mathrm{gameState}, G_t))\).

To run the autograder for this question and visualize the output:

python autograder.py -q q7

If you want to run this test (or any of the other tests) without graphics you can add the following flag:

python autograder.py -q q7 --no-graphics

As you watch the autograder output, remember that lighter squares indicate that pacman believes a ghost is more likely to occupy that location, and darker squares indicate a ghost is less likely to occupy that location. For which of the test cases do you notice differences emerging in the shading of the squares? Can you explain why some squares get lighter and some squares get darker?

Question 8 (1 point): Exact Inference Full Test

Now that Pacman knows how to use both his prior knowledge and his observations when figuring out where a ghost is, he is ready to hunt down ghosts on his own. We will use your observeUpdate and elapseTime implementations together to keep an updated belief distribution, and your simple greedy agent will choose an action based on the latest ditsibutions at each time step. In the simple greedy strategy, Pacman assumes that each ghost is in its most likely position according to his beliefs, then moves toward the closest ghost. Up to this point, Pacman has moved by randomly selecting a valid action.

Implement the chooseAction method in GreedyBustersAgent in bustersAgents.py. Your agent should first find the most likely position of each remaining uncaptured ghost, then choose an action that minimizes the maze distance to the closest ghost.

To find the maze distance between any two positions pos1 and pos2, use self.distancer.getDistance(pos1, pos2). To find the successor position of a position after an action:

successorPosition = Actions.getSuccessor(position, action)

You are provided with livingGhostPositionDistributions, a list of DiscreteDistribution objects representing the position belief distributions for each of the ghosts that are still uncaptured.

If correctly implemented, your agent should win the game in q8/3-gameScoreTest with a score greater than 700 at least 8 out of 10 times. Note: the autograder will also check the correctness of your inference directly, but the outcome of games is a reasonable sanity check.

We can represent how our greedy agent works with the following modification to the previous diagram:

Bayes net diagram

To run the autograder for this question and visualize the output:

python autograder.py -q q8

If you want to run this test (or any of the other tests) without graphics you can add the following flag:

python autograder.py -q q8 --no-graphics

Question 9 (2 points): Approximate Inference Initialization and Beliefs

Approximate inference is very trendy among ghost hunters this season. For the next few questions, you will implement a particle filtering algorithm for tracking a single ghost.

First, implement the functions initializeUniformly and getBeliefDistribution in the ParticleFilter class in inference.py. A particle (sample) is a ghost position in this inference problem. Note that, for initialization, particles should be evenly (not randomly) distributed across legal positions in order to ensure a uniform prior. We recommend thinking about how the mod operator is useful for initializeUniformly.

Note that 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 any other data type, such as a dictionary, is incorrect and will produce errors. The getBeliefDistribution method then takes the list of particles and converts it into a DiscreteDistribution object.

To test your code and run the autograder for this question:

python autograder.py -q q9

Question 10 (3 points): Approximate Inference Observation

Next, we will implement the observeUpdate method in the ParticleFilter class in inference.py. This method constructs a weight distribution over self.particles where the weight of a particle is the probability of the observation given Pacman’s position and that particle location. Then, we resample from this weighted distribution to construct our new list of particles.

You should again use the function self.getObservationProb to find the probability of an observation given Pacman’s position, a potential ghost position, and the jail position. The sample method of the DiscreteDistribution class will also be useful. As a reminder, you can obtain Pacman’s position using gameState.getPacmanPosition(), and the jail position using self.getJailPosition().

There is one special case that a correct implementation must handle. When all particles receive zero weight, the list of particles should be reinitialized by calling initializeUniformly. The total method of the DiscreteDistribution may be useful.

To run the autograder for this question and visualize the output:

python autograder.py -q q10

If you want to run this test (or any of the other tests) without graphics you can add the following flag:

python autograder.py -q q10 --no-graphics

Question 11 (3 points): Approximate Inference with Time Elapse

Implement the elapseTime function in the ParticleFilter class in inference.py. This function should construct a new list of particles that corresponds to each existing particle in self.particles advancing a time step, and then assign this new list back to self.particles. When complete, you should be able to track ghosts nearly as effectively as with exact inference.

Note that in this question, we will test both the elapseTime function in isolation, as well as the full implementation of the particle filter combining elapseTime and observe.

As in the elapseTime method of the ExactInference class, you should use:

newPosDist = self.getPositionDistribution(gameState, oldPos)

This line of code obtains the distribution over new positions for the ghost, given its previous position (oldPos). The sample method of the DiscreteDistribution class will also be useful.

To run the autograder for this question and visualize the output:

python autograder.py -q q11

If you want to run this test (or any of the other tests) without graphics you can add the following flag:

python autograder.py -q q11 --no-graphics

Note that even with no graphics, this test may take several minutes to run.

Submission

This is the second part of the GhostBuster project.

After you have successfully passed all test cases in your local autograder, you’re ready to prepare your project for submission. To do this, follow the steps below:

1. Generate a submission token: Run the following command in your terminal to create a token for submission:

    python submission_autograder.py
   

   If the script runs without any issues, it will produce a tracking.token file in your current directory.

   Note that this step can take several minutes to run. Please wait patiently.

2. Submit your project: Take the tracking.token file and upload it to the “Project 4” entry on Gradescope.

Remember, the tracking.token file is crucial for your project submission. It verifies your work on the autograder and is necessary for the evaluation process.