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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 square4 Mid-Semester Evaluations square4 Link is in your email square4 Assignments square4 W5 due tonight square4 W6 out tonight 2
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2 Decision Networks square4 MEU: choose the action which maximizes the expected utility given the evidence square4 Can directly operationalize this with decision networks square4 Bayes nets with nodes for utility and actions square4 Lets us calculate the expected utility for each action square4 New node types: square4 Chance nodes (just like BNs) square4 Actions (rectangles, cannot have parents, act as observed evidence) square4 Utility node (diamond, depends on action and chance nodes) Weather Forecast Umbrella U 4 Decision Networks square4 Action selection: square4 Instantiate all evidence square4 Set action node(s) each possible way square4 Calculate posterior for all parents of utility node, given the evidence square4 Calculate expected utility for each action square4 Choose maximizing action Weather Forecast Umbrella U 5
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3 Value of Information square4 Idea: compute value of acquiring evidence square4 Can be done directly from decision network square4 Example: buying oil drilling rights square4 Two blocks A and B, exactly one has oil, worth k square4 You can drill in one location square4 Prior probabilities 0.5 each, & mutually exclusive square4 Drilling in either A or B has MEU = k/2 square4 Question: what’s the value of information ? square4 Value of knowing which of A or B has oil square4 Value is expected gain in MEU from new info square4 Survey may say “oil in a” or “oil in b,” prob 0.5 each square4 If we know OilLoc, MEU is k (either way) square4 Gain in MEU from knowing OilLoc? square4 VPI(OilLoc) = k/2 square4 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 square4 Assume we have evidence E=e. Value if we act now: square4 Assume we see that E’ = e’. Value if we act then: square4 BUT E’ is a random variable whose value is unknown , so we don’t know what e’ will be square4 Expected value if E’ is revealed and then we act: square4 Value of information: how much MEU goes up by revealing E’ first: P(s | e) {e} a U {e,
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