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# Lecture-07-Adversarial search - CS 561 Artificial...

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CS 561: Artificial Intelligence Instructor: Sofus A. Macskassy, [email protected] TAs: Nadeesha Ranashinghe ( [email protected] ) William Yeoh ( [email protected] ) Harris Chiu ( [email protected] ) Lectures: MW 5:00-6:20pm, OHE 122 / DEN Office hours: By appointment Class page: http://www-rcf.usc.edu/~macskass/CS561-Spring2010/ This class will use http://www.uscden.net/ and class webpage - Up to date information - Lecture notes - Relevant dates, links, etc. Course material: [AIMA] Artificial Intelligence: A Modern Approach, by Stuart Russell and Peter Norvig. (2nd ed)

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This time: Outline (Adversarial Search AIMA Ch. 6] Game playing Perfect play The minimax algorithm alpha-beta pruning Resource limitations Elements of chance Imperfect information 2 CS561 - Lecture 7 - Macskassy - Spring 2010
What kind of games? Abstraction : To describe a game we must capture every relevant aspect of the game. Such as: Chess Tic-tac-toe Accessible environments: Such games are characterized by perfect information Search: game-playing then consists of a search through possible game positions Unpredictable opponent: introduces uncertainty thus game-playing must deal with contingency problems 3 CS561 - Lecture 7 - Macskassy - Spring 2010

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Searching for the next move Complexity: many games have a huge search space Chess: b = 35, m=100 nodes = 35 100 if each node takes about 1 ns to explore then each move will take about 10 50 millennia to calculate. Resource (e.g., time, memory) limit: optimal solution not feasible/possible, thus must approximate 1. Pruning: makes the search more efficient by discarding portions of the search tree that cannot improve quality result. 2. Evaluation functions: heuristics to evaluate utility of a state without exhaustive search. 4 CS561 - Lecture 7 - Macskassy - Spring 2010
Two-player games A game formulated as a search problem: Initial state: ? Operators: ? Terminal state: ? Utility function: ? 5 CS561 - Lecture 7 - Macskassy - Spring 2010

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Two-player games A game formulated as a search problem: Initial state: board position and turn Operators: definition of legal moves Terminal state: conditions for when game is over Utility function: a numeric value that describes the outcome of the game. E.g., -1, 0, 1 for loss, draw, win. (AKA payoff function ) 6 CS561 - Lecture 7 - Macskassy - Spring 2010
CS561 - Lecture 7 - Macskassy - Spring 2010 7 Games vs. search problems “Unpredictable" opponent solution is a strategy specifying a move for every possible opponent reply Time limits unlikely to find goal, must approximate Plan of attack: Computer considers possible lines of play (Babbage, 1846) Algorithm for perfect play (Zermelo, 1912; Von Neumann, 1944) Finite horizon, approximate evaluation (Zuse, 1945; Wiener, 1948; Shannon, 1950) First chess program (Turing, 1951) Machine learning to improve evaluation accuracy (Samuel, 1952- 57) Pruning to allow deeper search (McCarthy, 1956)

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Example: Tic-Tac-Toe 8 CS561 - Lecture 7 - Macskassy - Spring 2010
Type of games 9 CS561 - Lecture 7 - Macskassy - Spring 2010

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Type of games
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Lecture-07-Adversarial search - CS 561 Artificial...

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