Homework 2: Adversarial Search

Artificial Intelligence 
Homework 2: Adversarial Search

ACADEMIC HONESTY
As usual, the standard honor code and academic honesty policy applies. We run automated checks for
plagiarism to ensure only original work is given credit. Submissions isomorphic to (1) those that exist
anywhere online, (2) those submitted by classmates, or (3) those submitted by students in prior
semesters, will be considered plagiarism.
SUBMISSION
You will submit one zip file, named hw2_myUNI.zip, which contains two files:
- written.pdf, and
- driver.py or driver_3.py
You can submit as many times as you like before the deadline. Only your most recent submission will be
graded. The written submission can be handwritten and scanned (PDF scanning mobile apps typically
work well), or typed, but it must be legible in order to receive credit.
WRITTEN
Question 1: Association Rules
Consider the following items and transactions.
1. For a minimum support of 50%, use the Apriori algorithm to find all frequent itemsets in the
transaction table.
2. How many scans of the dataset were needed to find all frequent itemsets? What does this
number represent?
3. For a minimum confidence of 80%, use the Apriori algorithm to find all strong association rules
(report support and confidence) of the form:
Item 1 → Item 2 (support, confidence)
Item 1 and item 2 → item 3 (support, confidence)
4. Some variants of the Apriori algorithm leverage information provided by transaction identifiers
(TIDs). These variants associate each frequent k-itemset with the set of TIDs in which it appears.
For example, {diapers} is a frequent 1-itemset (set size of 1) and appears in the transactions with
TID’s {100, 300, 400, 500}, while the 1-itemset {coffee} appears in {100, 300, 500}.
a. How can information provided by the TID sets of the most frequent k-itemsets be used to
calculate the frequency of the potentially most frequent (k+1)-itemsets?
b. Does the Apriori step of generating frequent itemsets still require scanning the entire
transaction table? Discuss pros and cons of calculating frequency with this approach.
Question 2: Local Search Algorithms
There is a local search algorithm called simulated annealing which is based on statistical physics,
specifically thermodynamics. In this question, we ask you to:
1. Describe simulated annealing (3-6 sentences). Feel free to use the textbook and online sources.
2. Compare simulated annealing to the genetic algorithm, and give an example application of each
one. This paper provides a few examples:
https://pdfs.semanticscholar.org/e893/4a942f06ee91940ab57732953ec6a24b3f00.pdf.
Question 3: Minimax and Alpha-Beta Pruning
Consider the following search tree:
a. Using minimax, which of the three possible moves should MAX take at the root node? What is the
value of Max at the root?
b. Using minimax with alpha-beta pruning, compute the value of alpha and beta at each node.
Which branches are pruned?
Question 4: Iterative Deepening in Adversarial Search
Provide at least two reasons why Iterative Depth Search (also called Depth First Iterative Deepening
DFID) is useful in solving adversarial two-player games like chess.
Suggested reading: Section 7 of Depth-First Iterative Deepening Korf 1985, found here:
https://courseworks2.columbia.edu/courses/53318/files/folder/READING?preview=2364236
alpha = 1
beta = INF
alpha = -INF
beta = 1
alpha = 1
beta = -17
alpha = 1
beta = -2
PROGRAMMING
In this assignment, you will create an adversarial search agent to play the 2048-puzzle game. A demo of
the game is available here: gabrielecirulli.github.io/2048.
I. 2048 As A Two-Player Game
II. Choosing a Search Algorithm: Expectiminimax
III. Using The Skeleton Code
IV. What You Need To Submit
V. Important Information
VI. Before You Submit
I. 2048 As A Two-Player Game
2048 is played on a 4×4 grid with numbered tiles which can slide up, down, left, or right. This game can
be modeled as a two player game, in which the computer AI generates a 2- or 4-tile placed randomly on
the board, and the player then selects a direction to move the tiles. Note that the tiles move until they
either (1) collide with another tile, or (2) collide with the edge of the grid. If two tiles of the same number
collide in a move, they merge into a single tile valued at the sum of the two originals. The resulting tile
cannot merge with another tile again in the same move.
Usually, each role in a two-player games has a similar set of moves to choose from, and similar
objectives (e.g. chess). In 2048 however, the player roles are inherently asymmetric, as the Computer AI
places tiles and the Player moves them. Adversarial search can still be applied! Using your previous
experience with objects, states, nodes, functions, and implicit or explicit search trees, along with
our skeleton code, focus on optimizing your player algorithm to solve 2048 as efficiently and consistently
as possible.
II. Choosing A Search Algorithm: Expectiminimax
Review the lecture on adversarial search. Is 2048 a zero-sum game? What are the minimax and
expectiminimax principles?
The tile-generating Computer AI of 2048 is not particularly adversarial as it spawns tiles irrespective of
whether a spawn is the most adversarial to the user’s progress, with a 90% probability of a 2 and 10% for
a 4 (from GameManager.py). However, our Player AI will play as if the computer is adversarial since this
proves more effective in beating the game. We will specifically use the expectiminimax algorithm.
With expectiminimax, your game playing strategy assumes the Computer AI chooses a tile to place in a
way that minimizes the Player's outcome. Note whether or not the Computer AI is optimally adversarial is
a question to consider. As a general principle, how far the opponent's behavior deviates from the player’s
assumption certainly affects how well the AI performs. However you will see that this strategy works well
in this game.
.
Expectiminimax is a natural extension of the minimax algorithm, so think about how to implement minimax
first. As we saw in the simple case of tic-tac-toe, it is useful to employ the minimax algorithm assuming
the opponent is a perfect "minimizing" agent. In practice, an algorithm with the perfect opponent
assumption deviates from reality when playing a sub-par opponent making silly moves, but still leads to
the desired outcome of never losing. If the deviation goes the other way, however, (a "maximax"
opponent in which the opponent wants us to win), winning is obviously not guaranteed.
III. Using The Skeleton Code
The skeleton code includes the following files. Note that you will only be working in one of them, and the
rest are read-only:
● Read-only: GameManager.py. This is the driver program that loads your Computer AI and Player AI and
begins a game where they compete with each other. See below on how to execute this program.
● Read-only: Grid.py. This module defines the Grid object, along with some useful operations:
move(), getAvailableCells(), insertTile(), and clone(), which you may use in your code. These are by no
means the most efficient methods available, so if you wish to strive for better performance, feel free
to ignore these and write your own helper methods in a separate file.
● Read-only: BaseAI.py. This is the base class for any AI component. All AIs inherit from this module, and
implement the getMove() function, which takes a Grid object as parameter and returns a move (there are
different "moves" for different AIs).
● Read-only: ComputerAI.py. This inherits from BaseAI. The getMove() function returns a computer action
that is a tuple (x, y) indicating the place you want to place a tile.
● Writable: PlayerAI.py. You will create this file. The PlayerAI class should inherit from BaseAI. The
getMove() function to implement must return a number that indicates the player’s action. In particular, 0
stands for "Up", 1 stands for "Down", 2 stands for "Left", and 3 stands for "Right". This is where
your player-optimizing logic lives and is executed. Feel free to create submodules for this file to use, and
include any submodules in your submission.
● Read-only: BaseDisplayer.py and Displayer.py. These print the grid.
.
To test your code, execute the game manager like so: $ python GameManager.py
The progress of the game will be displayed on your terminal screen with one snapshot printed after
each move that the Computer AI or Player AI makes. Your Player AI is allowed 0.2 seconds to come up
with each move. The process continues until the game is over; that is, until no further legal moves can be
made. At the end of the game, the maximum tile value on the board is printed.
IMPORTANT: Do not modify the files that are specified as read-only. When your submission is graded,
the grader will first automatically over-write all read-only files in the directory before executing your code.
This is to ensure that all students are using the same game-play mechanism and computer opponent, and
that you cannot "work around" the skeleton program and manually output a high score.
IV. What You Need To Submit
Your job in this assignment is to write PlayerAI.py, which intelligently plays the 2048-puzzle game. Here is
a snippet of starter code to allow you to observe how the game looks when it is played out. In the
following "naive" Player AI. The getMove() function simply selects a next move in random out of the
available moves:
from random import randint
from BaseAI import BaseAI
class PlayerAI(BaseAI):
def getMove(self, grid):
moves = grid.getAvailableMoves()
return moves[randint(0, len(moves) - 1)] if moves else None
Of course, that is indeed a very naive way to play the 2048-puzzle game. If you submit this as your
finished product, you will likely receive a low grade. You should implement your Player AI with the
following points in mind:
● Employ the expectiminimax algorithm. This is a requirement. There are many viable strategies to beat
the 2048-puzzle game, but in this assignment we will be using he expectiminimax algorithm. Note that
90% of tiles placed by the computer are 2’s, while the remaining 10% are 4’s. It may be helpful to first
implement regular minimax.
● Implement alpha-beta pruning. This is a requirement. This should speed up the search process by
eliminating irrelevant branches. In this case, is there anything we can do about move ordering?
● Use heuristic functions. What is the maximum height of the game tree? Unlike elementary games like
tic-tac-toe, in this game it is highly impracticable to search the entire depth of the theoretical game tree.
To be able to cut off your search at any point, you must employ heuristic functions to allow you to
assign approximate values to nodes in the tree. Remember, the time limit allowed for each move is 0.2
seconds, so you must implement a systematic way to cut off your search before time runs out.
● Assign heuristic weights. You will likely want to include more than one heuristic function. In that case,
you will need to assign weights associated with each individual heuristic. Deciding on an appropriate set
of weights will take careful reasoning, along with careful experimentation. If you feel adventurous, you can
also simply write an optimization meta-algorithm to iterate over the space of weight vectors, until you
arrive at results that you are happy enough with.
V. Important Information
Please read the following information carefully. Before you post a clarifying question on the discussion
board, make sure that your question is not already answered in the following sections.
1. Note on Python 3
.
Each file in the skeleton code actually comes in two flavors: [filename].py (written in Python 2)
and [filename]_3.py (written in Python 3). If you prefer to develop in Python 3, you will be using the
latter version of each file in the skeleton code provided. In addition, you will have to name your player
AI file PlayerAI_3.py as well, so that the grader will be alerted to use the correct version of Python
during grading. For grading purposes, please only submit one of the following, but not both:
● PlayerAI.py (developed in Python 2, relying on the Python 2 version of each skeleton code file),
or
● PlayerAI_3.py (developed in Python 3, relying on the Python 3 version of each skeleton code file).
We will only grade one version if two are given.
To test your algorithm in Python 3, execute the game manager like so:
$ python3 GameManager_3.py
2. Basic Requirements
Your submission must fulfill the following requirements:
● You must use adversarial search in your PlayerAI (expectiminimax with alpha-beta pruning).
● You must provide your move within the time limit of 0.2 seconds.
● You must name your file PlayerAI.py (Python 2) or PlayerAI_3.py (Python 3).
● Your grade will depend on the maximum tile values your program usually gets to.
3. Grading Submissions
Grading is exceptionally straightforward for this project: the better your Player AI performs, the higher
your grade. While this is straightforward, we admit that this Adversarial Search project is the most difficult
project in this class because of its open-endedness. Your Player AI will be pitted against the standard
Computer AI for a total of 10 games, and the maximum tile value of each game will be recorded. Among
the 10 runs, we pick and average top 5 maximum tile values. Based on the average of these 5 maximum
tile values, your submission will be assessed out of a total of 100 points.
● Submissions that are no better than random will receive a score of zero.
● Submissions which contains two 1024 runs and three 2048 runs will receive full credit. For
example, [256, 512, 512, 512, 1024, 1024, 1024, 2048, 2048, 2048] will receive full credit.
● Submissions that fall somewhere in between will receive partial credit on a logarithmic scale.
That is, every time you manage to double your average maximum tile value, you will be moving
your final grade up in equally-spaced notches (instead of doubling as well). For other credit
examples, please see the FAQs.
VI. Before You Submit
● Make sure your code executes. In particular, make sure you name your file correctly according to
the instructions specified above, especially regarding different Python versions.
● Make sure your PlayerAI.py does not print anything to the screen. Printing gameplay progress is
handled by Grid.py, and there should ideally be nothing else printed.