Description
1 Introduction
I can hear you, ghost.
Running won’t save you from my
Particle filter!
Pacman spends his life running from ghosts, but things were not always so. Legend has it that many years
ago, Pacman’s great grandfather Grandpac learned to hunt ghosts for sport. However, he was blinded by
his power and could only track ghosts by their banging and clanging.
In this project, you will design Pacman agents that use sensors to locate and eat invisible ghosts. You’ll
advance from locating single, stationary ghosts to hunting packs of multiple moving ghosts with ruthless
efficiency.
The code for this project contains the following files, available as a zip archive.
Files you’ll edit:
bustersAgents.py Agents for playing the Ghostbusters variant of Pacman.
inference.py Code for tracking ghosts over time using their sounds.
Files you will not edit:
busters.py The main entry to Ghostbusters (replacing Pacman.py)
bustersGhostAgents.py New ghost agents for Ghostbusters
distanceCalculator.py Computes maze distances.
game.py Inner workings and helper classes for Pacman
ghostAgents.py Agents to control ghosts
graphicsDisplay.py Graphics for Pacman
graphicsUtils.py Support for Pacman graphics
layout.py Code for reading layout files and storing their contents
autograder.py Assignment autograder
util.py Utility functions
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Files to Edit and Submit: You will fill in portions of bustersAgents.py and inference.py during the
assignment. You should submit these files with your code and comments. Please do not change the other
files in this distribution or submit any of our original files other than these files.
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 the tests run by the autograder supplied in the zip file. If
all checks out with your code you will receive all of the points indicated by the autograder along with points
from the additional tests.
Getting Help: You are not alone! If you find 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 office hours. If you can’t make our office hours, let us know and we will arrange a different
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 the following files:
Your modified bustersAgents.py
Your modified inference.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.
Ghostbusters and BNs
In this assignment the goal is to hunt down scared but invisible ghosts. Pacman, ever resourceful, is equipped
with sonar (ears) that provides noisy readings of the Manhattan distance to each ghost. The game ends
when Pacman has eaten all the ghosts. To start, try playing a game yourself using the keyboard.
python2 busters.py
The blocks of color indicate where the each ghost could possibly be, given the noisy distance readings provided
to Pacman. The noisy distances at the bottom of the display are always non-negative, and always within 7
of the true distance. The probability of a distance reading decreases exponentially with its difference from
the true distance.
Your primary task in this project is to implement inference to track the ghosts. For the keyboard based
game above, a crude form of inference was implemented for you by default: all squares in which a ghost
could possibly be are shaded by the color of the ghost. Naturally, we want a better estimate of the ghost’s
position. Fortunately, Bayes’ Nets provide us with powerful tools for making the most of the information
we have. Throughout the rest of this project, you will implement algorithms for performing both exact and
approximate inference using Bayes’ Nets. The lab is challenging, so we do encouarge you to start early and
seek help when necessary.
While watching and debugging your code with the autograder, it will be helpful to have some understanding
of what the autograder is doing. There are 2 types of tests in this project, as differentiated by their *.test
files found in the subdirectories of the test_cases folder. For tests of class DoubleInferenceAgentTest,
you will see visualizations of the inference distributions generated by your code, but all Pacman actions
will be preselected according to the actions of the staff implementation. This is necessary in order to allow
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comparision of your distributions with the staff’s distributions. The second type of test is GameScoreTest,
in which your BustersAgent will actually select actions for Pacman and you will watch your Pacman play
and win games.
As you implement and debug your code, you may find it useful to run a single test at a time. In order to do
this you will need to use the -t flag with the autograder. For example if you only want to run the first test
of question 1, use:
python autograder.py -t test_cases/q1/1-ExactObserve
In general, all test cases can be found inside test_cases/q*.
Question 1 (3 points): Exact Inference Observation
In this question, you will update the observe 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. A
correct implementation should also handle one special case: when a ghost is eaten, you should place that
ghost in its prison cell, as described in the comments of observe.
To run the autograder for this question and visualize the output:
python autograder.py -q q1
As you watch the test cases, be sure that you understand how the squares converge to their final coloring.
In test cases where is Pacman boxed in (which is to say, he is unable to change his observation point), why
does Pacman sometimes have trouble finding the exact location of the ghost?
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 observe function, you’ll only see a single number even though there may
be multiple ghosts on the board.
Hints:
• You are implementing the online belief update for observing new evidence. Before any readings, Pacman
believes the ghost could be anywhere: a uniform prior (see initializeUniformly). After receiving a
reading, the observe function is called, which must update the belief at every position.
• Before typing any code, write down the equation of the inference problem you are trying to solve.
• Try printing noisyDistance, emissionModel, and PacmanPosition (in the observe function) to get
started.
• 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.
• Beliefs are stored as util.Counter objects (like dictionaries) in a field called self.beliefs, which
you should update.
• You should not need to store any evidence. The only thing you need to store in ExactInference is
self.beliefs.
Question 2 (4 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
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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 timestep.
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. Your agent has access to
the action distribution for any GhostAgent. In order to test your elapseTime implementation separately
from your observe implementation in the previous question, this question will not make use of your observe
implementation.
Since Pacman is not utilizing any observations about the ghost, this means that Pacman will start with
a uniform distribution over all spaces, and then update his beliefs according to how he knows the Ghost
is able to move. Since Pacman is not observing the ghost, this means the ghost’s 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 what Pacman already knows about their
valid movements.
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.
To run the autograder for this question and visualize the output:
python autograder.py -q q2
As an example of the GoSouthGhostAgent, you can run
python autograder.py -t test_cases/q2/2-ExactElapse
and observe that the distribution becomes concentrated at the bottom of the board.
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?
Hints:
• Instructions for obtaining a distribution over where a ghost will go next, given its current position and
the gameState, appears in the comments of ExactInference.elapseTime in inference.py.
• We assume that ghosts still move independently of one another, so although your code deals with one
ghost at a time, adding multiple ghosts should still work correctly.
Question 3 (3 points): 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. This question will use your observe and elapseTime
implementations together, along with a simple greedy hunting strategy which you will implement for this
question. In the simple greedy strategy, Pacman assumes that each ghost is in its most likely position
according to its beliefs, then moves toward the closest ghost. Up to this point, Pacman has moved by
randomly selecting a valid action.
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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 distance to the closest ghost. If correctly implemented, your agent should win the game in
q3/3-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.
To run the autograder for this question and visualize the output:
python autograder.py -q q3
Note: 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 q3 –no-graphics
Hints:
• When correctly implemented, your agent will thrash around a bit in order to capture a ghost.
• The comments of chooseAction provide you with useful method calls for computing maze distance
and successor positions.
• Make sure to only consider the living ghosts, as described in the comments.
Question 4 (3 points): Approximate Inference Observation
Approximate inference is very trendy among ghost hunters this season. Next, you will implement a particle
filtering algorithm for tracking a single ghost.
Implement the functions initializeUniformly, getBeliefDistribution, and observe for the ParticleFilter
class in inference.py. A correct implementation should also handle two special cases.
1. When all your particles receive zero weight based on the evidence, you should resample all particles
from the prior to recover.
2. When a ghost is eaten, you should update all particles to place that ghost in its prison cell, as described
in the comments of observe. When complete, you should be able to track ghosts nearly as effectively
as with exact inference.
To run the autograder for this question and visualize the output:
python autograder.py -q q4
Hints:
• A particle (sample) is a ghost position in this inference problem.
• The belief cloud generated by a particle filter will look noisy compared to the one for exact inference.
item util.sample or util.nSample will help you obtain samples from a distribution. If you use
util.sample and your implementation is timing out, try using util.nSample.
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Question 5 (4 points): Approximate Inference with Time Elapse
Implement the elapseTime function for the ParticleFilter class in inference.py. 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.
To run the autograder for this question and visualize the output:
python autograder.py -q q5
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. As an example, you can run
python autograder.py -t test_cases/q5/2-ParticleElapse
and observe that the distribution becomes concentrated at the bottom of the board.
Question 6 (4 points): Joint Particle Filter Observation
So far, we have tracked each ghost independently, which works fine for the default RandomGhost or more advanced DirectionalGhost. However, the prized DispersingGhost chooses actions that avoid other ghosts.
Since the ghosts’ transition models are no longer independent, all ghosts must be tracked jointly in a dynamic
Bayes net!
The Bayes net has the following structure, where the hidden variables G represent ghost positions and the
emission variables E are the noisy distances to each ghost. This structure can be extended to more ghosts,
but only two (a and b) are shown below.
You will now implement a particle filter that tracks multiple ghosts simultaneously. Each particle will
represent a tuple of ghost positions that is a sample of where all the ghosts are at the present time. The
code is already set up to extract marginal distributions about each ghost from the joint inference algorithm
you will create, so that belief clouds about individual ghosts can be displayed.
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Complete the initializeParticles, getBeliefDistribution, and observeState method in JointParticleFilter
to weight and resample the whole list of particles based on new evidence. As before, a correct implementation
should also handle two special cases.
1. When all your particles receive zero weight based on the evidence, you should resample all particles
from the prior to recover.
2. When a ghost is eaten, you should update all particles to place that ghost in its prison cell, as described
in the comments of observeState.
You should now effectively track dispersing ghosts. To run the autograder for this question and visualize the
output:
python autograder.py -q q6
Question 7 (4 points): Joint Particle Filter with Elapse Time
Complete the elapseTime method in JointParticleFilte in inference.py to resample each particle correctly for the Bayes net. In particular, each ghost should draw a new position conditioned on the positions
of all the ghosts at the previous time step. The comments in the method provide instructions for support
functions to help with sampling and creating the correct distribution.
Note that completing this question involves removing the call to util.raiseNotDefined(). This means
that the autograder will now grade both question 6 and question 7. Since these questions involve joint
distributions, they require more computational power (and time) to grade, so please be patient!
As you run the autograder note that q7/1-JointParticleElapse and q7/2-JointParticleElapse test
your elapseTime implementations only, and q7/3-JointParticleElapse tests both your elapseTime and
observe implementations. Notice the difference between test 1 and test 3. In both tests, pacman knows
that the ghosts will move to the sides of the gameboard. What is different between the tests, and why?
To run the autograder for this question use:
python autograder.py -q q7
Congratulations! That is the last assignment of the course!
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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 differ 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.
• If we find evidence of plagiarism we will investigate thoroughly and we will send your case to the
University Academic Offenses Office.
• Please do not implement your own ”improvement” to the search algorithms: it will wreak havoc with
the automarker. (Note, if you have invented a significant 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 submission.
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 difficulty completing
the assignment. Make sure you don’t find 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.
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