lecture 19

lecture 19 - CS 188: Artificial Intelligence Spring 2010...

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1 CS 188: Artificial Intelligence Spring 2010 Lecture 19: Decision Diagrams 4/1/2010 Pieter Abbeel – UC Berkeley Many slides over this course adapted from Dan Klein, Stuart Russell, Andrew Moore Announcements s Mid-Semester Evaluations s Link is in your email s Assignments s W5 due tonight s W6 out tonight 2
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2 Decision Networks s MEU: choose the action which maximizes the expected utility given the evidence s Can directly operationalize this with decision networks s Bayes nets with nodes for utility and actions s Lets us calculate the expected utility for each action s New node types: s Chance nodes (just like BNs) s Actions (rectangles, cannot have parents, act as observed evidence) s Utility node (diamond, depends on action and chance nodes) Weather Forecast Umbrella U 4 Decision Networks s Action selection: s Instantiate all evidence s Set action node(s) each possible way s Calculate posterior for all parents of utility node, given the evidence s Calculate expected utility for each action s Choose maximizing action Weather Forecast Umbrella U 5
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3 Value of Information s Idea: compute value of acquiring evidence s Can be done directly from decision network s Example: buying oil drilling rights s Two blocks A and B, exactly one has oil, worth k s You can drill in one location s Prior probabilities 0.5 each, & mutually exclusive s Drilling in either A or B has MEU = k/2 s Question: what’s the value of information ? s Value of knowing which of A or B has oil s Value is expected gain in MEU from new info s Survey may say “oil in a” or “oil in b,” prob 0.5 each s If we know OilLoc, MEU is k (either way) s Gain in MEU from knowing OilLoc? s VPI(OilLoc) = k/2 s Fair price of information: k/2 OilLoc DrillLoc U D O U a a k a b 0 b a 0 b b k O P a 1/2 b 1/2 12 Value of Information s Assume we have evidence E=e. Value if we act now: s Assume we see that E’ = e’. Value if we act then: s BUT E’ is a random variable whose value is unknown , so we don’t know what e’ will be s Expected value if E’ is revealed and then we act: s Value of information: how much MEU goes up by revealing E’ first: P(s | e) {e} a U {e, e’ } a P(s | e, e’ ) U {e} P( e’ | e) {e, e’ }
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This note was uploaded on 04/21/2010 for the course EECS 188 taught by Professor Cs188 during the Spring '01 term at Berkeley.

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lecture 19 - CS 188: Artificial Intelligence Spring 2010...

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