I can hear you, ghost.
Running won't save you from my
Question 1 (10 points) Compute (showing your work) the predicted distribution over states at time 2. (This is the case where we have not made any observations yet.)
Question 2 (10 points) Suppose that the observation at time 1 is a, and the observation at time 2 is b. Compute (showing your work) the distribution over states at time 2 after making these observations.
Question 3 (10 points) Compute the smoothed state distribution at time step 1 after observing a at time step 1 and b at time step 2.
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 assignment, 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 assignment contains the following files, available as a zip archive.
||Agents for playing the Ghostbusters variant of Pacman.|
||Code for tracking ghosts over time using their sounds.|
||The main entry to Ghostbusters (replacing Pacman.py)|
||New ghost agents for Ghostbusters|
||Computes maze distances|
||Inner workings and helper classes for Pacman|
||Agents to control ghosts|
||Graphics for Pacman|
||Support for Pacman graphics|
||Keyboard interfaces to control Pacman|
||Code for reading layout files and storing their contents|
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
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.
In our 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 implementation task in this assignment 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.
python busters.py -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.
Hint:As you're debugging, you'll find it useful to actually see where the ghost is. Use option
-s, when running Pacman
python busters.py -s -k 1
Question 4 (10 points) Update the
observe method in
ExactInference class of
inference.py to correctly update the agent's
belief distribution over ghost positions. 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. 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
StationaryGhost ghost agents don't move,
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.
initializeUniformly). After receiving a reading, the
observefunction is called, which must update the belief at every position.
observefunction) to get started.
util.Counterobjects (like dictionaries) in a field called
self.beliefs, which you should update.
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 and ghosts move.
Question 5 (10 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. To test it out, you can
DirectionalGhost ghost agent, which causes the ghosts to move in a somewhat
predictable fashion. If you don't include
-g DirectionalGhost, then the ghost will
move randomly, which will be harder to track, though it should still be possible.
python busters.py -s -k 1 -g DirectionalGhost
python busters.py -s -k 1
gameState, appears in the comments of
DirectionalGhostis 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.
Now that Pacman 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 Pacman assumes that each ghost is in its most likely position according to its beliefs, then moves toward the closest ghost.
Question 6 (10 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. Note: the autograder will check the
correctness of your inference directly, not the outcome of games, but it's a reasonable sanity check.
python busters.py -p GreedyBustersAgent -l smallHuntHints:
chooseActionprovide you with useful method calls for computing maze distance and successor positions.