MyPawns OppPawns MyKings OppKings MyThreatened OppThreatened MyWins OppWins Draws
|
|
- Kimberly Horton
- 5 years ago
- Views:
Transcription
1 The Role of Opponent Skill Level in Automated Game Learning Ying Ge and Michael Hash Advisor: Dr. Mark Burge Armstrong Atlantic State University Savannah, Geogia USA Abstract- This paper explores the role of opponent skill level in automated game learning. The game of checkers was chosen as our experiment model. With the standard linear polynomial approach to evaluate the board state and a Least Mean Square (LMS) rule to update the weights, we trained a naive checkers program to play by having it play against: a naive random computer player, against another naive player who learned to play the game with exactly the same algorithm, and against an expert computer player. The results show that the program learned effectively using the above algorithm, but an over-fitting problem occurred approximately after 2 to 3 games in all three scenarios. The use of a smaller update rate significantly delayed the overfitting problem. We also observed that playing against an expert actually slowed down the learning process for a naive player. This is somewhat analogous to human learning: a naive chess player will learn little by playing the master Kasparov. Our finding was that playing against a random player with a small update rate is a very effective method for a beginner to learn to play the game in our current model. In addition, the learning process can be improved by incorporating the MINMAX look-ahead algorithm. 1 Introduction This experiment was initially conducted to help understand a model of machine learning based on Mitchell's design [1]. We modified a random checker player program written in C at the University of Massachusetts. Then we applied the linear polynomial approach to evaluate the board state after each move and the Least Mean Square (LMS) rule to update the weights of that polynomial. Our modified learning players played against each other on a UNIX machine for several days and nights. Aplayer from the top five was chosen to be our expert player for this paper. 1.1 Learning Model In order to teach the computer to pick the best next move at a certain board state, we needed a representation of the current board state and an evaluation of the future board state after the move. There are some interesting board features with respect to the relative piece positions. For example, a board position can be expressed in terms of the first and higher moments of the white and black pieces separately about two orthogonal axes on the board. Our program uses a simple and common representation. The board was represented by the quantity of six features: x 1 x 2 x 3 x 4 x 5 x 6 : The number of my pawns : The number of opponent pawns : The number of my kings : The number of opponent kings : The number of pieces threatened by the opponent : The numberofopponent pieces threatened by me The evaluation of the board was represented by the linear combination of the above six features: V (b)=w+w1 x1+w2 x2+w3 x3+w4 x4+w5 x5+w6 x6;
2 where w i are the weights to be learned. We arbitrarily defined the final board state's evaluation value to be V(b) = 1 (won the game), V(b) = -1 (lost the game), and V(b) = (tie). Our computer player would pick the next move that led to the biggest board value V(b) since V(b) = 1 was defined as winning. For each game played, we recorded all of the board states until the end and updated the weights using the difference of the real board value and the trained board value derived from V (b) =w + w 1 x 1 + w 2 x 2 + w 3 x 3 + w 4 x 4 + w 5 x 5 + w 6 x 6 : We used the LMS weight update rule: w i = w i + (V t rain(b) V (b)) x i : 1.2 Experiment Approaches Throughout our experiment, we kept human learning in mind. Thinking of human situations in game playing, we let the naive computer program learn to play checkers by playing against a random player who randomly chose the next legal move, by playing against a learning pl ayer who had the same algorithm as ours, and finally by playing against an expert player who had won most of the games with many different types of players on a network for several days and nights. The results of how the machine learned show both differences and similarities to human players. 2 Learning Results The results provided in this document are primarily in graph form. The learning weights for each of the 6 features are presented: my pawn, opponent pawn, my king, opponent king, my threatened, and opponent threatened. Also, to observe the performance, the numbers of winning, losing, and tied games were graphed. For each of the following three learning experiences, 1, 5, and 1 games were tested. Only the pertinent results are presented. 2.1 Playing Against A Random Player The random player picked the next move randomly as long as it was legal. It had no sense of which boards were more likely to lead to a win. Results show that the machine learned very quickly and started to defeat the opponent after only a few games. The weights were changing in the correct direction. My Pawns and My Kings were weighted positively while Opponent Pawns and Opponent Kings were weighted negatively. My Threatened was weighted negatively. This means that the program had learned the piece advantages on the board, i.e. My Kings, My Pawns were desirable and threatened pieces were not. However, there was an over-fitting phenomenon observed: the key weights, My Pawns and Opponent Pawns began to head in the wrong direction after approximately 2-3 games and then fluctuated all the way till the end. From the game results graph, we can see that although the total number of games won is bigger than the random opponent's, the performance started decaying after the weights were over-fitted Figure 1: All six weights adjusting for 1 games against random player Figure 2: The distribution of games won for 1 against random player Figure 3: All six weights adjusting for 5 games against random player.
3 Figure 4: The distribution of games won for 5 against random player Figure 6: The distribution of games won for 5 against learning player. 2.2 Playing Against A Learning Player In the second experiment, we cloned a new learning player with exactly the same learning algorithm and data representation scheme. This time, the overall games won were not fixed to either of the player, which was consistent with the prediction derived from the human situation. Two competitors with the same strategy and strengths impaired the decision to choose an absolute winner? The over-fitting problem still existed. Weights started to fluctuate after about 25 games. In addition, the weights became unreasonable. 2.3 Playing Against An Expert Player The idea of this experiment came from the fact that human beginners learn very little, when playing experts, because they get beaten so quickly. We therefore conducted this experiment to see how a machine learned to play against an expert. Not surprisingly, the outcome was similar to the real world situation. Our player was beaten badly all the way through. Especially at the beginning stage, the weights hesitated to grow fast in the desired direction. It indicates that our player was not certain which board states were bad states. This was probably caused by early losses. From the weights graph, we can see the player later learned to play better, but overall performance never exceeded the expert's Figure 5: All six weights adjusting for 5 games against learning player Figure 7: All six weights adjusting for 1 games against expert player.
4 Figure 8: The distribution of games won for 1 against expert player Figure 1: The distribution of games won for 1 against random player with small update rate. 2.4 Fixing The Over-Fitting Problem Over-fitting is not an uncommon problem in artificial intelligence models. For example, neural networks and decision trees all have this problem of over-fitting the training data [1]. There are several ways to solve the problem. For instance, a decaying method can be used to reduce the update rate along the number of games played. What we did in this experiment was simply to use a much smaller update rate all the way through (We changed the update rate from.11 to.111). Although it delayed the over-fitting problem, it caused longer learning time since every improvement was very tiny and cautious. The following graphs against a random player show the steady improvement ofthelearn- ing weights. There was no over-fitting problem observed even after playing 1 games. 3 Improving The Algorithm From the above, we learned that a small update rate can improve the learning by avoiding over-fitting. In addition, the algorithm can be further improved by incorporating MIN-MAX look-ahead method. When our computer player decides to pick the next best legal move, instead of calculating only the immediate resulting board values and picking the best one, now he will look several moves ahead and calculate the resulting board values several steps ahead. Theoretically, he could see far ahead until the game is over (win, lose, or tie) and pick the winning path among this humongous decision tree Figure 9: All six weights adjusting for 1 games against random player with small update rate. Figure 11: A tree of moves which might be investigated during the look-ahead procedure. The actual branchings are much more numerous than those shown, and the tree is apt to extend to as many as2levels.
5 Figure 12: Simplified diagram showing how the evaluations are backed up through the "tree" of possible moves to arrive at the best next move. The evaluation starts at (3). When we, humans play games, we try to look ahead as many moves as possible. The average person can look ahead about 2 moves, Kasparov can probably look ahead 4 or 5 moves. How far can a machine look ahead? It depends on the complexity of different games. The computational space and time are limited in a real game. Alpha-Beta Pruning can reduce the complexity from, O(b d )too(b 1 2 ) where b is the average branches of each node and d is the depth of the tree [2]. 4 Conclusion The above experiments revealed some familiar issues in machine learning. Over-fitting is a common problem. Careful choice of an updating rate can solve or ease the problem. Human learning usually does not suffer from the over-fitting that is common in machine learning. However, machine players and human players show some similarities in the way they learn to play the game. For instance, playing against experts does not help a beginner to learn effectively. Because of the early defeats, beginners seem to hesitate to take any dramatic steps. References [1] Mitchell, Tom M. Machine Learning [2] Norving, Peter and Russell, Stuart. Artificial Intelligence: A Modern Approach
ARTIFICIAL INTELLIGENCE (CS 370D)
Princess Nora University Faculty of Computer & Information Systems ARTIFICIAL INTELLIGENCE (CS 370D) (CHAPTER-5) ADVERSARIAL SEARCH ADVERSARIAL SEARCH Optimal decisions Min algorithm α-β pruning Imperfect,
More informationGame-playing: DeepBlue and AlphaGo
Game-playing: DeepBlue and AlphaGo Brief history of gameplaying frontiers 1990s: Othello world champions refuse to play computers 1994: Chinook defeats Checkers world champion 1997: DeepBlue defeats world
More informationGame Playing AI. Dr. Baldassano Yu s Elite Education
Game Playing AI Dr. Baldassano chrisb@princeton.edu Yu s Elite Education Last 2 weeks recap: Graphs Graphs represent pairwise relationships Directed/undirected, weighted/unweights Common algorithms: Shortest
More informationV. Adamchik Data Structures. Game Trees. Lecture 1. Apr. 05, Plan: 1. Introduction. 2. Game of NIM. 3. Minimax
Game Trees Lecture 1 Apr. 05, 2005 Plan: 1. Introduction 2. Game of NIM 3. Minimax V. Adamchik 2 ü Introduction The search problems we have studied so far assume that the situation is not going to change.
More informationADVERSARIAL SEARCH. Today. Reading. Goals. AIMA Chapter Read , Skim 5.7
ADVERSARIAL SEARCH Today Reading AIMA Chapter Read 5.1-5.5, Skim 5.7 Goals Introduce adversarial games Minimax as an optimal strategy Alpha-beta pruning 1 Adversarial Games People like games! Games are
More informationFoundations of AI. 6. Adversarial Search. Search Strategies for Games, Games with Chance, State of the Art. Wolfram Burgard & Bernhard Nebel
Foundations of AI 6. Adversarial Search Search Strategies for Games, Games with Chance, State of the Art Wolfram Burgard & Bernhard Nebel Contents Game Theory Board Games Minimax Search Alpha-Beta Search
More informationFoundations of AI. 5. Board Games. Search Strategies for Games, Games with Chance, State of the Art. Wolfram Burgard and Luc De Raedt SA-1
Foundations of AI 5. Board Games Search Strategies for Games, Games with Chance, State of the Art Wolfram Burgard and Luc De Raedt SA-1 Contents Board Games Minimax Search Alpha-Beta Search Games with
More informationArtificial Intelligence. Minimax and alpha-beta pruning
Artificial Intelligence Minimax and alpha-beta pruning In which we examine the problems that arise when we try to plan ahead to get the best result in a world that includes a hostile agent (other agent
More informationAdversarial Search: Game Playing. Reading: Chapter
Adversarial Search: Game Playing Reading: Chapter 6.5-6.8 1 Games and AI Easy to represent, abstract, precise rules One of the first tasks undertaken by AI (since 1950) Better than humans in Othello and
More informationData Structures and Algorithms
Data Structures and Algorithms CS245-2015S-P4 Two Player Games David Galles Department of Computer Science University of San Francisco P4-0: Overview Example games (board splitting, chess, Network) /Max
More informationCS 771 Artificial Intelligence. Adversarial Search
CS 771 Artificial Intelligence Adversarial Search Typical assumptions Two agents whose actions alternate Utility values for each agent are the opposite of the other This creates the adversarial situation
More informationCS885 Reinforcement Learning Lecture 13c: June 13, Adversarial Search [RusNor] Sec
CS885 Reinforcement Learning Lecture 13c: June 13, 2018 Adversarial Search [RusNor] Sec. 5.1-5.4 CS885 Spring 2018 Pascal Poupart 1 Outline Minimax search Evaluation functions Alpha-beta pruning CS885
More informationADVERSARIAL SEARCH. Today. Reading. Goals. AIMA Chapter , 5.7,5.8
ADVERSARIAL SEARCH Today Reading AIMA Chapter 5.1-5.5, 5.7,5.8 Goals Introduce adversarial games Minimax as an optimal strategy Alpha-beta pruning (Real-time decisions) 1 Questions to ask Were there any
More informationGame-playing AIs: Games and Adversarial Search I AIMA
Game-playing AIs: Games and Adversarial Search I AIMA 5.1-5.2 Games: Outline of Unit Part I: Games as Search Motivation Game-playing AI successes Game Trees Evaluation Functions Part II: Adversarial Search
More informationLecture 33: How can computation Win games against you? Chess: Mechanical Turk
4/2/0 CS 202 Introduction to Computation " UNIVERSITY of WISCONSIN-MADISON Computer Sciences Department Lecture 33: How can computation Win games against you? Professor Andrea Arpaci-Dusseau Spring 200
More informationCPS 570: Artificial Intelligence Two-player, zero-sum, perfect-information Games
CPS 57: Artificial Intelligence Two-player, zero-sum, perfect-information Games Instructor: Vincent Conitzer Game playing Rich tradition of creating game-playing programs in AI Many similarities to search
More informationAdversarial Search and Game- Playing C H A P T E R 6 C M P T : S P R I N G H A S S A N K H O S R A V I
Adversarial Search and Game- Playing C H A P T E R 6 C M P T 3 1 0 : S P R I N G 2 0 1 1 H A S S A N K H O S R A V I Adversarial Search Examine the problems that arise when we try to plan ahead in a world
More informationLearning to Play like an Othello Master CS 229 Project Report. Shir Aharon, Amanda Chang, Kent Koyanagi
Learning to Play like an Othello Master CS 229 Project Report December 13, 213 1 Abstract This project aims to train a machine to strategically play the game of Othello using machine learning. Prior to
More informationToday. Types of Game. Games and Search 1/18/2010. COMP210: Artificial Intelligence. Lecture 10. Game playing
COMP10: Artificial Intelligence Lecture 10. Game playing Trevor Bench-Capon Room 15, Ashton Building Today We will look at how search can be applied to playing games Types of Games Perfect play minimax
More informationCMPUT 396 Tic-Tac-Toe Game
CMPUT 396 Tic-Tac-Toe Game Recall minimax: - For a game tree, we find the root minimax from leaf values - With minimax we can always determine the score and can use a bottom-up approach Why use minimax?
More informationAdversarial Search. CMPSCI 383 September 29, 2011
Adversarial Search CMPSCI 383 September 29, 2011 1 Why are games interesting to AI? Simple to represent and reason about Must consider the moves of an adversary Time constraints Russell & Norvig say: Games,
More informationGame Engineering CS F-24 Board / Strategy Games
Game Engineering CS420-2014F-24 Board / Strategy Games David Galles Department of Computer Science University of San Francisco 24-0: Overview Example games (board splitting, chess, Othello) /Max trees
More informationAdversarial Search. Human-aware Robotics. 2018/01/25 Chapter 5 in R&N 3rd Ø Announcement: Slides for this lecture are here:
Adversarial Search 2018/01/25 Chapter 5 in R&N 3rd Ø Announcement: q Slides for this lecture are here: http://www.public.asu.edu/~yzhan442/teaching/cse471/lectures/adversarial.pdf Slides are largely based
More informationArtificial Intelligence Search III
Artificial Intelligence Search III Lecture 5 Content: Search III Quick Review on Lecture 4 Why Study Games? Game Playing as Search Special Characteristics of Game Playing Search Ingredients of 2-Person
More informationCOMP219: COMP219: Artificial Intelligence Artificial Intelligence Dr. Annabel Latham Lecture 12: Game Playing Overview Games and Search
COMP19: Artificial Intelligence COMP19: Artificial Intelligence Dr. Annabel Latham Room.05 Ashton Building Department of Computer Science University of Liverpool Lecture 1: Game Playing 1 Overview Last
More informationAdversarial Search (Game Playing)
Artificial Intelligence Adversarial Search (Game Playing) Chapter 5 Adapted from materials by Tim Finin, Marie desjardins, and Charles R. Dyer Outline Game playing State of the art and resources Framework
More informationgame tree complete all possible moves
Game Trees Game Tree A game tree is a tree the nodes of which are positions in a game and edges are moves. The complete game tree for a game is the game tree starting at the initial position and containing
More informationGames (adversarial search problems)
Mustafa Jarrar: Lecture Notes on Games, Birzeit University, Palestine Fall Semester, 204 Artificial Intelligence Chapter 6 Games (adversarial search problems) Dr. Mustafa Jarrar Sina Institute, University
More informationCS188 Spring 2014 Section 3: Games
CS188 Spring 2014 Section 3: Games 1 Nearly Zero Sum Games The standard Minimax algorithm calculates worst-case values in a zero-sum two player game, i.e. a game in which for all terminal states s, the
More informationProgramming an Othello AI Michael An (man4), Evan Liang (liange)
Programming an Othello AI Michael An (man4), Evan Liang (liange) 1 Introduction Othello is a two player board game played on an 8 8 grid. Players take turns placing stones with their assigned color (black
More informationCS 331: Artificial Intelligence Adversarial Search II. Outline
CS 331: Artificial Intelligence Adversarial Search II 1 Outline 1. Evaluation Functions 2. State-of-the-art game playing programs 3. 2 player zero-sum finite stochastic games of perfect information 2 1
More informationGame Playing. Garry Kasparov and Deep Blue. 1997, GM Gabriel Schwartzman's Chess Camera, courtesy IBM.
Game Playing Garry Kasparov and Deep Blue. 1997, GM Gabriel Schwartzman's Chess Camera, courtesy IBM. Game Playing In most tree search scenarios, we have assumed the situation is not going to change whilst
More informationSet 4: Game-Playing. ICS 271 Fall 2017 Kalev Kask
Set 4: Game-Playing ICS 271 Fall 2017 Kalev Kask Overview Computer programs that play 2-player games game-playing as search with the complication of an opponent General principles of game-playing and search
More informationMachine Learning Othello Project
Machine Learning Othello Project Tom Barry The assignment. We have been provided with a genetic programming framework written in Java and an intelligent Othello player( EDGAR ) as well a random player.
More informationIntroduction Mitchell, Chapter 1. CptS 570 Machine Learning School of EECS Washington State University
Introduction Mitchell, Chapter 1 CptS 570 Machine Learning School of EECS Washington State University Outline Why machine learning Some examples Relevant disciplines What is a well-defined learning problem
More informationAdversary Search. Ref: Chapter 5
Adversary Search Ref: Chapter 5 1 Games & A.I. Easy to measure success Easy to represent states Small number of operators Comparison against humans is possible. Many games can be modeled very easily, although
More informationFoundations of Artificial Intelligence
Foundations of Artificial Intelligence 6. Board Games Search Strategies for Games, Games with Chance, State of the Art Joschka Boedecker and Wolfram Burgard and Bernhard Nebel Albert-Ludwigs-Universität
More informationFoundations of AI. 6. Board Games. Search Strategies for Games, Games with Chance, State of the Art
Foundations of AI 6. Board Games Search Strategies for Games, Games with Chance, State of the Art Wolfram Burgard, Andreas Karwath, Bernhard Nebel, and Martin Riedmiller SA-1 Contents Board Games Minimax
More informationModule 3. Problem Solving using Search- (Two agent) Version 2 CSE IIT, Kharagpur
Module 3 Problem Solving using Search- (Two agent) 3.1 Instructional Objective The students should understand the formulation of multi-agent search and in detail two-agent search. Students should b familiar
More informationAr#ficial)Intelligence!!
Introduc*on! Ar#ficial)Intelligence!! Roman Barták Department of Theoretical Computer Science and Mathematical Logic So far we assumed a single-agent environment, but what if there are more agents and
More informationCS 2710 Foundations of AI. Lecture 9. Adversarial search. CS 2710 Foundations of AI. Game search
CS 2710 Foundations of AI Lecture 9 Adversarial search Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square CS 2710 Foundations of AI Game search Game-playing programs developed by AI researchers since
More informationFoundations of Artificial Intelligence
Foundations of Artificial Intelligence 6. Board Games Search Strategies for Games, Games with Chance, State of the Art Joschka Boedecker and Wolfram Burgard and Frank Hutter and Bernhard Nebel Albert-Ludwigs-Universität
More informationSchool of EECS Washington State University. Artificial Intelligence
School of EECS Washington State University Artificial Intelligence 1 } Classic AI challenge Easy to represent Difficult to solve } Zero-sum games Total final reward to all players is constant } Perfect
More informationCS188 Spring 2010 Section 3: Game Trees
CS188 Spring 2010 Section 3: Game Trees 1 Warm-Up: Column-Row You have a 3x3 matrix of values like the one below. In a somewhat boring game, player A first selects a row, and then player B selects a column.
More informationCS 188: Artificial Intelligence Spring Announcements
CS 188: Artificial Intelligence Spring 2011 Lecture 7: Minimax and Alpha-Beta Search 2/9/2011 Pieter Abbeel UC Berkeley Many slides adapted from Dan Klein 1 Announcements W1 out and due Monday 4:59pm P2
More informationAnnouncements. CS 188: Artificial Intelligence Spring Game Playing State-of-the-Art. Overview. Game Playing. GamesCrafters
CS 188: Artificial Intelligence Spring 2011 Announcements W1 out and due Monday 4:59pm P2 out and due next week Friday 4:59pm Lecture 7: Mini and Alpha-Beta Search 2/9/2011 Pieter Abbeel UC Berkeley Many
More informationOutline. Game Playing. Game Problems. Game Problems. Types of games Playing a perfect game. Playing an imperfect game
Outline Game Playing ECE457 Applied Artificial Intelligence Fall 2007 Lecture #5 Types of games Playing a perfect game Minimax search Alpha-beta pruning Playing an imperfect game Real-time Imperfect information
More informationGames CSE 473. Kasparov Vs. Deep Junior August 2, 2003 Match ends in a 3 / 3 tie!
Games CSE 473 Kasparov Vs. Deep Junior August 2, 2003 Match ends in a 3 / 3 tie! Games in AI In AI, games usually refers to deteristic, turntaking, two-player, zero-sum games of perfect information Deteristic:
More informationAnnouncements. Homework 1. Project 1. Due tonight at 11:59pm. Due Friday 2/8 at 4:00pm. Electronic HW1 Written HW1
Announcements Homework 1 Due tonight at 11:59pm Project 1 Electronic HW1 Written HW1 Due Friday 2/8 at 4:00pm CS 188: Artificial Intelligence Adversarial Search and Game Trees Instructors: Sergey Levine
More informationGame playing. Chapter 5, Sections 1 6
Game playing Chapter 5, Sections 1 6 Artificial Intelligence, spring 2013, Peter Ljunglöf; based on AIMA Slides c Stuart Russel and Peter Norvig, 2004 Chapter 5, Sections 1 6 1 Outline Games Perfect play
More informationContents. Foundations of Artificial Intelligence. Problems. Why Board Games?
Contents Foundations of Artificial Intelligence 6. Board Games Search Strategies for Games, Games with Chance, State of the Art Wolfram Burgard, Bernhard Nebel, and Martin Riedmiller Albert-Ludwigs-Universität
More informationAdversarial Search. Soleymani. Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 5
Adversarial Search CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2017 Soleymani Artificial Intelligence: A Modern Approach, 3 rd Edition, Chapter 5 Outline Game
More informationProgramming Project 1: Pacman (Due )
Programming Project 1: Pacman (Due 8.2.18) Registration to the exams 521495A: Artificial Intelligence Adversarial Search (Min-Max) Lectured by Abdenour Hadid Adjunct Professor, CMVS, University of Oulu
More informationCOMP219: Artificial Intelligence. Lecture 13: Game Playing
CMP219: Artificial Intelligence Lecture 13: Game Playing 1 verview Last time Search with partial/no observations Belief states Incremental belief state search Determinism vs non-determinism Today We will
More informationArtificial Intelligence Lecture 3
Artificial Intelligence Lecture 3 The problem Depth first Not optimal Uses O(n) space Optimal Uses O(B n ) space Can we combine the advantages of both approaches? 2 Iterative deepening (IDA) Let M be a
More informationMonte Carlo Tree Search
Monte Carlo Tree Search 1 By the end, you will know Why we use Monte Carlo Search Trees The pros and cons of MCTS How it is applied to Super Mario Brothers and Alpha Go 2 Outline I. Pre-MCTS Algorithms
More informationPrepared by Vaishnavi Moorthy Asst Prof- Dept of Cse
UNIT II-REPRESENTATION OF KNOWLEDGE (9 hours) Game playing - Knowledge representation, Knowledge representation using Predicate logic, Introduction tounit-2 predicate calculus, Resolution, Use of predicate
More informationGame Playing. Philipp Koehn. 29 September 2015
Game Playing Philipp Koehn 29 September 2015 Outline 1 Games Perfect play minimax decisions α β pruning Resource limits and approximate evaluation Games of chance Games of imperfect information 2 games
More informationGame Playing State-of-the-Art CSE 473: Artificial Intelligence Fall Deterministic Games. Zero-Sum Games 10/13/17. Adversarial Search
CSE 473: Artificial Intelligence Fall 2017 Adversarial Search Mini, pruning, Expecti Dieter Fox Based on slides adapted Luke Zettlemoyer, Dan Klein, Pieter Abbeel, Dan Weld, Stuart Russell or Andrew Moore
More informationCS 380: ARTIFICIAL INTELLIGENCE MONTE CARLO SEARCH. Santiago Ontañón
CS 380: ARTIFICIAL INTELLIGENCE MONTE CARLO SEARCH Santiago Ontañón so367@drexel.edu Recall: Adversarial Search Idea: When there is only one agent in the world, we can solve problems using DFS, BFS, ID,
More informationAndrei Behel AC-43И 1
Andrei Behel AC-43И 1 History The game of Go originated in China more than 2,500 years ago. The rules of the game are simple: Players take turns to place black or white stones on a board, trying to capture
More informationAlgorithms for Data Structures: Search for Games. Phillip Smith 27/11/13
Algorithms for Data Structures: Search for Games Phillip Smith 27/11/13 Search for Games Following this lecture you should be able to: Understand the search process in games How an AI decides on the best
More informationThe game of Reversi was invented around 1880 by two. Englishmen, Lewis Waterman and John W. Mollett. It later became
Reversi Meng Tran tranm@seas.upenn.edu Faculty Advisor: Dr. Barry Silverman Abstract: The game of Reversi was invented around 1880 by two Englishmen, Lewis Waterman and John W. Mollett. It later became
More informationCS 5522: Artificial Intelligence II
CS 5522: Artificial Intelligence II Adversarial Search Instructor: Alan Ritter Ohio State University [These slides were adapted from CS188 Intro to AI at UC Berkeley. All materials available at http://ai.berkeley.edu.]
More informationGame-playing AIs: Games and Adversarial Search FINAL SET (w/ pruning study examples) AIMA
Game-playing AIs: Games and Adversarial Search FINAL SET (w/ pruning study examples) AIMA 5.1-5.2 Games: Outline of Unit Part I: Games as Search Motivation Game-playing AI successes Game Trees Evaluation
More informationCS 1571 Introduction to AI Lecture 12. Adversarial search. CS 1571 Intro to AI. Announcements
CS 171 Introduction to AI Lecture 1 Adversarial search Milos Hauskrecht milos@cs.pitt.edu 39 Sennott Square Announcements Homework assignment is out Programming and experiments Simulated annealing + Genetic
More informationCSE 40171: Artificial Intelligence. Adversarial Search: Games and Optimality
CSE 40171: Artificial Intelligence Adversarial Search: Games and Optimality 1 What is a game? Game Playing State-of-the-Art Checkers: 1950: First computer player. 1994: First computer champion: Chinook
More informationDocumentation and Discussion
1 of 9 11/7/2007 1:21 AM ASSIGNMENT 2 SUBJECT CODE: CS 6300 SUBJECT: ARTIFICIAL INTELLIGENCE LEENA KORA EMAIL:leenak@cs.utah.edu Unid: u0527667 TEEKO GAME IMPLEMENTATION Documentation and Discussion 1.
More informationMore on games (Ch )
More on games (Ch. 5.4-5.6) Announcements Midterm next Tuesday: covers weeks 1-4 (Chapters 1-4) Take the full class period Open book/notes (can use ebook) ^^ No programing/code, internet searches or friends
More informationFoundations of Artificial Intelligence
Foundations of Artificial Intelligence 42. Board Games: Alpha-Beta Search Malte Helmert University of Basel May 16, 2018 Board Games: Overview chapter overview: 40. Introduction and State of the Art 41.
More informationExperiments on Alternatives to Minimax
Experiments on Alternatives to Minimax Dana Nau University of Maryland Paul Purdom Indiana University April 23, 1993 Chun-Hung Tzeng Ball State University Abstract In the field of Artificial Intelligence,
More informationComputer Science and Software Engineering University of Wisconsin - Platteville. 4. Game Play. CS 3030 Lecture Notes Yan Shi UW-Platteville
Computer Science and Software Engineering University of Wisconsin - Platteville 4. Game Play CS 3030 Lecture Notes Yan Shi UW-Platteville Read: Textbook Chapter 6 What kind of games? 2-player games Zero-sum
More informationGame-Playing & Adversarial Search
Game-Playing & Adversarial Search This lecture topic: Game-Playing & Adversarial Search (two lectures) Chapter 5.1-5.5 Next lecture topic: Constraint Satisfaction Problems (two lectures) Chapter 6.1-6.4,
More informationCMSC 671 Project Report- Google AI Challenge: Planet Wars
1. Introduction Purpose The purpose of the project is to apply relevant AI techniques learned during the course with a view to develop an intelligent game playing bot for the game of Planet Wars. Planet
More informationCPS331 Lecture: Search in Games last revised 2/16/10
CPS331 Lecture: Search in Games last revised 2/16/10 Objectives: 1. To introduce mini-max search 2. To introduce the use of static evaluation functions 3. To introduce alpha-beta pruning Materials: 1.
More informationGame Playing for a Variant of Mancala Board Game (Pallanguzhi)
Game Playing for a Variant of Mancala Board Game (Pallanguzhi) Varsha Sankar (SUNet ID: svarsha) 1. INTRODUCTION Game playing is a very interesting area in the field of Artificial Intelligence presently.
More informationGame Playing AI Class 8 Ch , 5.4.1, 5.5
Game Playing AI Class Ch. 5.-5., 5.4., 5.5 Bookkeeping HW Due 0/, :59pm Remaining CSP questions? Cynthia Matuszek CMSC 6 Based on slides by Marie desjardin, Francisco Iacobelli Today s Class Clear criteria
More informationGame Playing State-of-the-Art. CS 188: Artificial Intelligence. Behavior from Computation. Video of Demo Mystery Pacman. Adversarial Search
CS 188: Artificial Intelligence Adversarial Search Instructor: Marco Alvarez University of Rhode Island (These slides were created/modified by Dan Klein, Pieter Abbeel, Anca Dragan for CS188 at UC Berkeley)
More informationCSE 573: Artificial Intelligence Autumn 2010
CSE 573: Artificial Intelligence Autumn 2010 Lecture 4: Adversarial Search 10/12/2009 Luke Zettlemoyer Based on slides from Dan Klein Many slides over the course adapted from either Stuart Russell or Andrew
More information2048: An Autonomous Solver
2048: An Autonomous Solver Final Project in Introduction to Artificial Intelligence ABSTRACT. Our goal in this project was to create an automatic solver for the wellknown game 2048 and to analyze how different
More informationMore on games (Ch )
More on games (Ch. 5.4-5.6) Alpha-beta pruning Previously on CSci 4511... We talked about how to modify the minimax algorithm to prune only bad searches (i.e. alpha-beta pruning) This rule of checking
More informationArtificial Intelligence. Topic 5. Game playing
Artificial Intelligence Topic 5 Game playing broadening our world view dealing with incompleteness why play games? perfect decisions the Minimax algorithm dealing with resource limits evaluation functions
More informationGames and Adversarial Search II
Games and Adversarial Search II Alpha-Beta Pruning (AIMA 5.3) Some slides adapted from Richard Lathrop, USC/ISI, CS 271 Review: The Minimax Rule Idea: Make the best move for MAX assuming that MIN always
More informationCS 4700: Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 10 Today Adversarial search (R&N Ch 5) Tuesday, March 7 Knowledge Representation and Reasoning (R&N Ch 7)
More informationCS 188: Artificial Intelligence Spring Game Playing in Practice
CS 188: Artificial Intelligence Spring 2006 Lecture 23: Games 4/18/2006 Dan Klein UC Berkeley Game Playing in Practice Checkers: Chinook ended 40-year-reign of human world champion Marion Tinsley in 1994.
More informationCS221 Project Final Report Gomoku Game Agent
CS221 Project Final Report Gomoku Game Agent Qiao Tan qtan@stanford.edu Xiaoti Hu xiaotihu@stanford.edu 1 Introduction Gomoku, also know as five-in-a-row, is a strategy board game which is traditionally
More informationComputer Game Programming Board Games
1-466 Computer Game Programg Board Games Maxim Likhachev Robotics Institute Carnegie Mellon University There Are Still Board Games Maxim Likhachev Carnegie Mellon University 2 Classes of Board Games Two
More informationAdversarial Search 1
Adversarial Search 1 Adversarial Search The ghosts trying to make pacman loose Can not come up with a giant program that plans to the end, because of the ghosts and their actions Goal: Eat lots of dots
More informationFor slightly more detailed instructions on how to play, visit:
Introduction to Artificial Intelligence CS 151 Programming Assignment 2 Mancala!! The purpose of this assignment is to program some of the search algorithms and game playing strategies that we have learned
More information2 person perfect information
Why Study Games? Games offer: Intellectual Engagement Abstraction Representability Performance Measure Not all games are suitable for AI research. We will restrict ourselves to 2 person perfect information
More informationCS 188: Artificial Intelligence. Overview
CS 188: Artificial Intelligence Lecture 6 and 7: Search for Games Pieter Abbeel UC Berkeley Many slides adapted from Dan Klein 1 Overview Deterministic zero-sum games Minimax Limited depth and evaluation
More informationMinimax Trees: Utility Evaluation, Tree Evaluation, Pruning
Minimax Trees: Utility Evaluation, Tree Evaluation, Pruning CSCE 315 Programming Studio Fall 2017 Project 2, Lecture 2 Adapted from slides of Yoonsuck Choe, John Keyser Two-Person Perfect Information Deterministic
More informationLocal Search. Hill Climbing. Hill Climbing Diagram. Simulated Annealing. Simulated Annealing. Introduction to Artificial Intelligence
Introduction to Artificial Intelligence V22.0472-001 Fall 2009 Lecture 6: Adversarial Search Local Search Queue-based algorithms keep fallback options (backtracking) Local search: improve what you have
More informationCSE 40171: Artificial Intelligence. Adversarial Search: Game Trees, Alpha-Beta Pruning; Imperfect Decisions
CSE 40171: Artificial Intelligence Adversarial Search: Game Trees, Alpha-Beta Pruning; Imperfect Decisions 30 4-2 4 max min -1-2 4 9??? Image credit: Dan Klein and Pieter Abbeel, UC Berkeley CS 188 31
More information4. Games and search. Lecture Artificial Intelligence (4ov / 8op)
4. Games and search 4.1 Search problems State space search find a (shortest) path from the initial state to the goal state. Constraint satisfaction find a value assignment to a set of variables so that
More informationFive-In-Row with Local Evaluation and Beam Search
Five-In-Row with Local Evaluation and Beam Search Jiun-Hung Chen and Adrienne X. Wang jhchen@cs axwang@cs Abstract This report provides a brief overview of the game of five-in-row, also known as Go-Moku,
More informationGame Playing. Dr. Richard J. Povinelli. Page 1. rev 1.1, 9/14/2003
Game Playing Dr. Richard J. Povinelli rev 1.1, 9/14/2003 Page 1 Objectives You should be able to provide a definition of a game. be able to evaluate, compare, and implement the minmax and alpha-beta algorithms,
More informationCS 188: Artificial Intelligence
CS 188: Artificial Intelligence Adversarial Search Prof. Scott Niekum The University of Texas at Austin [These slides are based on those of Dan Klein and Pieter Abbeel for CS188 Intro to AI at UC Berkeley.
More informationCS 229 Final Project: Using Reinforcement Learning to Play Othello
CS 229 Final Project: Using Reinforcement Learning to Play Othello Kevin Fry Frank Zheng Xianming Li ID: kfry ID: fzheng ID: xmli 16 December 2016 Abstract We built an AI that learned to play Othello.
More informationAdversarial Search. Chapter 5. Mausam (Based on slides of Stuart Russell, Andrew Parks, Henry Kautz, Linda Shapiro) 1
Adversarial Search Chapter 5 Mausam (Based on slides of Stuart Russell, Andrew Parks, Henry Kautz, Linda Shapiro) 1 Game Playing Why do AI researchers study game playing? 1. It s a good reasoning problem,
More information