Assignment 2 Solution

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Description

Part 1: Programming

You are going to do the 5 programming questions about search given here: http://ai.berkeley.edu/ multiagent.html. You are only required to change multiAgents.py. If you have any issues with other parts of the code let your instructor or TA know ASAP, even if you manage to solve your problem. Use the data structures in util.py for the autograder to work properly. If the you think you have the right answer but the autograder is not giving you any points, try to run it on individual questions (look at P0 for details on how to use the autograder.py).

In the previous homework, HW1, you had the option to use the mazeDistance, which gives you the cost to go between 2 locations in the maze taking the walls into account, i.e., the true graph cost. This

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results in better cost estimates at the expense of more computation. This resulted in lower number of node expansions but potentially made the algorithms run slower than if you used the manhattanDistance. Feel free to use either, however, make sure that your code does not take too long!

Hints

There are hints for the programming part, especially about what features to use in your evaluation functions, in the project description website. Read those carefully, as they generally provide good ideas. Note that your evaluation function for question 1 is a good starting point for question 5. As noted in the website, do not waste too much time on both of these questions and only get back to them if you have time left.

Evaluation Functions

The evaluationFunction method of the ReflexAgent class already shows you how to get important information from theGameState class. As an addition, you can use the getCapsules method to get the locations of the remaining capsules as a list. These capsules let the pacman eat the ghosts for signi cant additional points!

You can call the asList method of the Food class to get the locations of the foods as a list. You can use the built-in len function to get the remaining number of foods or capsules. The scaredTimes gives you the remaining time for pacman to eat the ghosts. A 0 value means that the ghosts are not scared so watch out!

You are potentially going to use the distances to the food as a feature (e.g. the distance to the closest food). Your agent, pacman, might get right next to the food and not eat it! This is due to the fact that your evaluation function might return a lower value after eating the food and the next distance to the closest food or the average distance to the foods becomes higher. Make sure your evalation function takes this into account. The same thing might happen with eating the ghosts, pacman might chase the ghost but never actually eat it.

Your pacman can get to a state of thrashing, which means that it either stops or keeps moving be-tween two states, until a ghost comes nearby. In your ReflexAgent, you might think of penalizing the Stop action. This is not the best ideaand there are other things you can do. If you happen to have this problem, try to tune your feature weights. Finally, it is okay if you do not have the best agent behavior as we are not sending a rover to Mars, yet.

Programming for Multiple Ghosts

Remember that in the class we talked about the multiplayer case, where all the agents are trying to maximize their utility. Think of all the ghosts as trying to minimize your evaluation function, i.e., all the ghosts are MIN agents. This means that you need to call the min-value function for all of the ghosts.You can do it by passing an agent index to your value function. Note that pacman will always be agent 0. Look at the comments in the multiAgents.py le to see which functions take an agent index (look for agentIndex) as a variable. You are free to de ne your own functions, either externally or within the classes, but make sure the entry points are in the existing class methods (e.g. the getAction methods).

Keeping Track of Depth

In this assignment, 1-level of depth is interpreted as including all the agents actions. In the 2-player version, this means 1-level of depth is completed after you check the actions of both the MAX agent and the MIN agent. If you have more than 1 ghost, the depth increases after you look at the actions of pacman and all the ghosts.

In the class, we have discussed why we are not able to search as deep as the end of the game. The assignment requires you to implement a depth limit. In a recursive algorithm, it might not be obvious how to implement this. There are multiple ways to do this. You can pass down a depth variable, along with your state to your functions.

Alpha-Beta Pruning

The and the values are not for the entire search tree but for a certain node. This means that you should not keep the same variables for the entire search.

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Pacman Not Eating the Last Food

Due to the setup of the environment, you might not be able to force the pacman to eat the last food for the programming question 5. This is because the action sequences Stop and Move, where the latter is moving in any legal direction, and Move and Stop will potentially have the same value at the end of the game depending on the location of the ghosts. Since the Stop always comes before the Move actions when getting the legal actions, your agent might always chose it rst. Keep this in mind if your pacman stops right next to a food at the end of a game. A way to solve this is to force pacman to chose the Move action in case two actions have the same value.

Part 2: Report

This part includes answering the following questions based on your programs output on the given pacman tests.

You are expected to answer the questions concisely. Five sentences is more than enough for most of them. Limit yourself to 200 words. It is okay if you over-generalize, as long as your direction is clear and correct. Note that some answers are already in the provided link to the Berkeley site. For some questions, you do not even need to write that much (Hint: Q2, Q3 and Q4). Note that some of the answers could already be in the provided link to the Berkeley site! Answers that are longer than 200 words may not be graded!

Create a PDF le named report.pdf containing your answers for submission.

Written Q1:

What are the features you used in your evaluation function for your re ex agent? Why did you chose them? If you have too many, limit yourself to at most 5. Do you think using the reciprocals or negatives of some values is a good idea and why?

Written Q2:

Try the following lines of code:

python pacman.py -p MinimaxAgent -l trickyClassic -a depth=2 -f python pacman.py -p AlphaBetaAgent -l trickyClassic -a depth=2 -f

Run both them until 20 seconds (or less if pacman ends up dieing) and see how far the pacman has got. You do not need to write additional time keeping code, a stopwatch should su ce.

In your tests, were you able to see any speed di erence between the MinimaxAgent and AlphaBetaAgent, between pacman actions? If so, why and if not why not? Is there any situation you came across that highlights this?

Written Q3:

When you were running the tests in the previous question, did your pacman behave exactly in both cases? Why?

Written Q4:

Now try the same with the ExpectimaxAgent;

python pacman.py -p ExpectimaxAgent -l trickyClassic -a depth=2 -f

Comment on how fast your code runs. Compare it with the MinimaxAgent and AlphaBetaAgent. Note that this comparison is trickier to do. If you are not able to conclusively see anything, write what you would have expected.

Written Q5:

We are sure that you were able to write a better evaluation function than the one we used for the pro-gramming questions 2-4. Did you change anything from your evaluation function for the Re exAgent? If so, what were the changes? What, if anything, is di erent in this case? If you have written something entirely di erent, comment on your new evaluation function.

Written Q6:

For both the programming questions 1 and 5, you probably needed to tune your feature weights. If so,

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comment on how you selected your weights, what did you prioritize and why.

Submission

You are going to submit a compressed archive through the blackboard site. The le should extract to a folder with your student ID without the leading zeros. This folder should only contain report.pdf and multiAgents.py. Other les will be deleted and/or overwritten. Do not submit any code if you only want us to grade your report.

Important: Download your submission to make sure it is not corrupted and it has your latest report/code. You are only going to be graded by your blackboard submission.

Submission Instructions

You are going to submit a compressed archive through the blackboard site. The le can have zip, rar, tar, rar, tar.gz or 7z format.

This compressed le should extract to a folder with your student identi cation number with the two leading zeros removed which should have 5 digits. Multiple folders (apart from operating system ones such as MACOSX or DS Store) greatly slows us down and as such will result in penalties

Code that does not run or that does not terminate will not receive any credits.

Do not trust the way that your operating system extracts your le. They will mostly put the contents inside a folder with the same name as the compressed le. We are going to call a program (based on your le extension) from the command line. The safest way is to put everyting inside a folder with your ID, then compress the folder and give it your ID as its name.

Once you are sure about your assignment and the compressed le, submit it through Blackboard. After you submit your code, download it and check if it is the one you intended to submit.

DO NOT SUBMIT CODE THAT DOES NOT TERMINATE OR THAT BLOWS UP THE MEMORY.

Let us know if you need any help with setting up your compressed le. This is very important. We will put all of your compressed les into a folder and run multiple scripts to extract, clean up, grade and do plagiarism checking. If you do not follow the above instructions, then scripts might fail. If these scripts fail then you will receive a 0 from the coding part and the report will be worth 1/3 of your grade.

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