Project 4: Ghostbusters
(Thanks to John DeNero and Dan Klein.)
I can hear you, ghost.
Running won't save you from my
Due November 18th, 2014, 2:30pm
Pac-Man spends his life running from ghosts, but things were not always so. Legend has it that many years
ago, Pac-Man'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 Pac-Man 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:
Files you will edit
|Agents for playing the Ghostbusters variant of Pac-Man.
|Code for tracking ghosts over time using their sounds.
Files you will not edit
What to submit: You will fill in portions of
inference.py during the assignment. You should submit this file with your code and comments.
Please do not change the other files in this distribution or submit any of our original files other
bustersAgents.py. This assignment is submitted with the usual svn commands.
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. We mean it. -- You can probably find solutions for this assignment online. This assignment is only worth about 1/10 of your final grade. If you use those online solutions, we will probably detect it.
Getting Help: You are not alone! If you find yourself stuck on something,
contact the course staff for help. Office hours, section, and the newsgroup 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.
Ghostbusters and BNs
In the cse511a version of Ghostbusters, the goal is to hunt down scared but invisible ghosts.
Pac-Man, 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.
The blocks of color indicate where the each ghost could possibly be, given the noisy distance
readings provided to Pac-Man. 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.
A crude form of inference is implemented for you by default: all squares in which a
ghost could possibly be are shaded by the color of the ghost. Option
shows where the ghost actually is.
python busters.py -s -k 1
Naturally, we want a better estimate of the ghost's position. We will start by locating a
single, stationary ghost using multiple noisy distance readings. The default
bustersAgents.py uses the
ExactInference module in
inference.py to track ghosts.
Question 1 (3 points) Update the
observe method in
ExactInference class of
inference.py to correctly update the agent's
belief distribution over ghost positions. When complete, you should be able to accurately locate a
ghost by circling it.
python busters.py -s -k 1 -g StationaryGhost
Because the default
RandomGhost ghost agents move independently of one another,
you can track each one separately. The default
BustersKeyboardAgent is set up to
do this for you. Hence, you should be able to locate multiple stationary ghosts simultaneously.
Encircling the ghosts should give you precise distributions over the ghosts' locations.
python busters.py -s -g StationaryGhost
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.
- 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
- Before typing any code, write down the equation of the inference problem you are
trying to solve.
- Try printing
pacmanPosition (in the
observe function) to get
- In the Pac-Man 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
self.beliefs, which you should update.
- You should not need to store any evidence. The only thing you need to store in
Ghosts don't hold still forever. Fortunately, your agent has access to the action distribution
GhostAgent. Your next task is to use the ghost's move distribution to update
your agent's beliefs when time elapses.
Question 2 (4 points) Fill in the
elapseTime method in
ExactInference to correctly update the agent's belief distribution over the ghost's
position when the ghost moves. When complete, you should be able to accurately locate moving ghosts,
but some uncertainty will always remain about a ghost's position as it moves.
python busters.py -s -k 1
python busters.py -s -k 1 -g DirectionalGhost
- Instructions for obtaining a distribution over where a ghost will go next, given its current
position and the
gameState, appears in the comments of
DirectionalGhost is easier to track because it is more predictable.
After running away from one for a while, your agent should have a good idea where it is.
- We assume that ghosts still move independently of one another, so while you can develop all
of your code for one ghost at a time, adding multiple ghosts should still work correctly.
Now that Pac-Man can track ghosts, try playing without peeking at the ghost locations. Beliefs about each ghost will be overlaid on the screen. The game should be challenging, but not impossible.
python busters.py -l bigHunt
Now, pacman is ready to hunt down ghosts on his own. You will implement a simple greedy hunting strategy, where Pac-Man assumes that each ghost is in its most likely position according to its beliefs, then moves toward the closest ghost.
Question 3 (4 points) Implement the
chooseAction method 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
smallHunt with a score greater than 700 at least
8 out of 10 times.
python busters.py -p GreedyBustersAgent -l smallHunt
- 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.
Approximate inference is very trendy among ghost hunters this season. Next, you will implement a particle filtering algorithm for tracking a single ghost.
Question 4 (5 points) Implement all necessary methods for the
ParticleFilter class in
inference.py. When complete, you should be able to track ghosts nearly as effectively as with exact inference. This means that your agent should win the default layout with
a score greater than 100 at least 8 out of 10 times.
python busters.py -k 1 -s -a inference=ParticleFilter
- 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.
- To debug, you may want to start with
The Dispersing Ghost
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!
Since the ghosts move in sequence, the Bayes net has the following structure, where the hidden variables G represent ghost positions and the emission variables are the noisy distances to each ghost. This structure can be extended to more ghosts, but only two 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.
Question 5 (3 points) Complete the
elapseTime method in
inference.py to resample each particle correctly for the Bayes net. The comments in the method provide instructions for helpful support functions. With only this part of the particle filter completed, you should be able to predict that ghosts will flee to the perimeter of the layout to avoid each other, though you won't know which ghost is in which corner (see image).
python busters.py -s -a inference=MarginalInference -g DispersingGhost
Question 6 (6 points) Complete the
observeState method in
JointParticleFilter to weight and resample the whole list of particles based on new evidence. 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. If correctly implemented, your agent should win the default layout with a 10-game average score greater than 480.
python busters.py -s -k 3 -a inference=MarginalInference -g DispersingGhost