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Lecture 22-Rational Decisions

Lecture 22-Rational Decisions - 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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CS561 - Lecture 22 - Macskassy - Spring 2010 2 Rational Decisions [AIMA Ch. 16] Rational preferences Utilities Money Multi-attribute utilities Decision networks Value of information
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CS561 - Lecture 22 - Macskassy - Spring 2010 3 Preferences An agent chooses among prizes ( A , B , etc.) and lotteries , i.e., situations with uncertain prizes Lottery L = [p, A; (1-p), B] Notation: A Â B A preferred to B A » B indifference between A and B A B B not preferred to A » Â
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CS561 - Lecture 22 - Macskassy - Spring 2010 4 Rational preferences Idea: preferences of a rational agent must obey constraints. Rational preferences ) behavior describable as maximization of expected utility Constraints: Orderability (A Â B) _ (B Â A) _ (A » B) Transitivity (A Â B) ^ (B Â C) ) (A Â C) Continuity A Â B Â C ) 9 p [p, A; 1-p,C] » B Substitutability A » B ) [p, A; 1-p,C] » [p, B; 1-p,C] Monotonicity A Â B ) (p ¸ q , [p,A; 1-p,B] [q, A; 1-q, B]) Decomposability [p, A; 1-p, [q, B, (1-q), C]]) » [p, A; (1-p)q, B; (1-p)(1-q), C] » Â
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CS561 - Lecture 22 - Macskassy - Spring 2010 5 Decomposability A “complex” hierarchical lottery can be collapsed into a single multi-choice lottery: L A B C p 1-p q 1-q L A B C p (1-p)q (1-p)(1-q) [p, A; 1-p, [q, B, (1-q), C]] [p, A; (1-p)q, B; (1-p)(1-q), C]
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