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.
Ghostbusters and BNs
In the Pacman 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.
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 encourage 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 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:
python autograder.py -t test_cases/q1/1-ExactUpdate
In general, all test cases can be found inside test_cases/q*.
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. Take a look at the
total functions that have been provided.
Question 1 (3 points): Exact Inference Observation
In this question, you will update 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. A correct implementation should also handle one special case: when a ghost is eaten, you should place that ghost in its jail cell, as described in the comments of
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: 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 q1 --no-graphics
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.
- 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
observeUpdatefunction 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.
- You should use the function
self.getObservationProbwhich 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
- 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 in a
util.Counterobject (similar to a dictionary) 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
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