Project 4: Ghostbusters

Project 4: Ghostbusters 
Table of Contents
Introduction
Welcome
Q0: DiscreteDistribution Class
Q1: Observation Probability
Q2: Exact Inference Observation
Q3: Exact Inference with Time Elapse
Q4: Exact Inference Full Test
Q5: Approximate Inference Initialization and Beliefs
Q6: Approximate Inference Observation
Q7: Approximate Inference with Time Elapse
Q8: Joint Particle Filter Initialization
Q9: Joint Particle Filter Observation
Q10: Joint Particle Filter Time Elapse and Full Test
I can hear you, ghost.
Running won't save you from my
Particle filter!
Introduction
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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/ghostbusters.zip).
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
keyboardAgents.py Keyboard interfaces to control Pacman
layout.py Code for reading layout files and storing their contents
util.py Utility functions
Files to Edit and Submit: You will fill in portions of bustersAgents.py and
inference.py during the assignment. 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
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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 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 BNs
In the CS 188 version of Ghostbusters, 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.
python3 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 project 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 , your will see visualizations of the inference
distributions generated by your code, but all Pacman actions will be preselected File failed to load: https://courses.cs.washington.edu/courses/cse573/20wi/project4/files/extensions/MathZoom.js
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according to the actions of the staff implementation. This is necessary in order
to allow 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:
python3 autograder.py -t test_cases/q1/1-ObsProb
In general, all test cases can be found inside test_cases/q*.
For this project, it is possible sometimes for the autograder to time out if
running the tests with graphics. To accurately determine whether or not your
code is efficient enough, you should run the tests with the --no-graphics flag.
If the autograder passes with this flag, then you will receive full points, even if
the autograder times out with graphics.
Question 0 (0 points): DiscreteDistribution Class
Throughout this 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.
There are no autograder tests for this question, but the correctness of your
implementation can be easily checked. We have provided Python doctests
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feel free to add more and implement other tests of your own. You can run the
doctests using:
python3 -m doctest -v inference.py
Note that, depending on the implementation details of the sample method,
some correct implementations may not pass the doctests that are provided. To
thoroughly check the correctness of your sample method, you should instead
draw many samples and see if the frequency of each key converges to be
proportional of its corresponding value.
Question 1 (2 points): 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 P(noisyDistance |
pacmanPosition, 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 P(noisyDistance | 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. So, if the
ghost's position is the jail position, then the observation is None with
probability 1, and everything else with probability 0. Conversely, if the distance
reading is not None , then the ghost is in jail with probability 0. If the distance
reading is None, then the ghost is in jail with probability 1. Make sure you
handle this special case in your implementation.
To test your code and run the autograder for this question:
python3 autograder.py -q q1
As a general note, it is possible for some of the autograder tests to take a long
time to run for this project, and you will have to exercise patience. As long as
the autograder doesn't time out, you should be fine (provided that you actually
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Question 2 (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
observe 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 update 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:
python3 autograder.py -q q2
If you want to run this test (or any of the other tests) without graphics you can
add the following flag:
python3 autograder.py -q q2 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
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Question 3 (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, 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
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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:
python3 autograder.py -q q3
If you want to run this test (or any of the other tests) without graphics you can
add the following flag:
python3 autograder.py -q q3 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with 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 4 (2 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 observeUpdate 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 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)
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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 q4/3-
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:
python3 autograder.py -q q4
If you want to run this test (or any of the other tests) without graphics you can
add the following flag:
python3 autograder.py -q q4 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
Question 5 (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.
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:
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python3 autograder.py -q q5
Question 6 (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:
python3 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:
python3 autograder.py -q q6 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
Question 7 (3 points): Approximate Inference with Time
Elapse
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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:
python3 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:
python3 autograder.py -q q7 --no-graphics
Note that even with no graphics, this test may take several minutes to run.
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
Question 8 (1 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
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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.
Complete the initializeUniformly method in JointParticleFilter in
inference.py . Your initialization should be consistent with a uniform prior. You
may find the Python itertools package helpful. Specifically, look at
itertools.product to get an implementation of the Cartesian product.
However, note that, if you use this, the permutations are not returned in a
random order. Therefore, you must then shuffle the list of permutations in order
to ensure even placement of particles across the board.
As before, use self.legalPositions to obtain a list of positions a ghost may
occupy. Also as before, the variable you store your particles in must be a
list.
To run the autograder for this question and visualize the output:
python3 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:
python3 autograder.py -q q8 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
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your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
Question 9 (3 points): Joint Particle Filter Observation
In this question, you will complete the observeUpdate method in the
JointParticleFilter class of inference.py . A correct implementation will
weight and resample the entire list of particles based on the observation of all
ghost distances.
To loop over all the ghosts, use:
for i in range(self.numGhosts):
 ...
You can still obtain Pacman's position using gameState.getPacmanPosition() ,
but to get the jail position for a ghost, use self.getJailPosition(i) , since now
there are multiple ghosts each with their own jail positions.
Your implementation should also again handle the special case when all
particles receive zero weight. In this case, self.particles should be
recreated from the prior distribution by calling initializeUniformly .
As in the update method for the ParticleFilter class, 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.
To run the autograder for this question and visualize the output:
python3 autograder.py -q q9
If you want to run this test (or any of the other tests) without graphics you can
add the following flag:
python3 autograder.py -q q9 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
File failed to load: https://courses.cs.washington.edu/courses/cse573/20wi/project4/files/extensions/MathZoom.js
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Question 10 (3 points): Joint Particle Filter Time Elapse
and Full Test
Complete the elapseTime method in JointParticleFilter 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.
As in the last question, you can loop over the ghosts using:
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:
newPosDist = self.getPositionDistribution(gameState, prevGhostPositions, i, self.ghostAgents[i])
Note that completing this question involves grading both question 9 and
question 10. 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 q10/1-JointParticlePredict and q10/2-
JointParticlePredict test your predict implementations only, and q10/3-
JointParticleFull tests both your predict and update 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?
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To run the autograder for this question and visualize the output:
python3 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:
python3 autograder.py -q q10 --no-graphics
*IMPORTANT*: In general, it is possible sometimes for the autograder to time
out if running the tests with graphics. To accurately determine whether or not
your code is efficient enough, you should run the tests with the --no-graphics
flag. If the autograder passes with this flag, then you will receive full points,
even if the autograder times out with graphics.
Submission
Submit bustersAgents.py and inference.py to Project 4 on Canvas.
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