Maximum Expected Utility Acting Probabilistic Graphical Models Decision Making Maximum Expected Utility

Simple Decision Making A simple decision making situation D: A set of possible actions Val(A)={a1,…,aK} A set of states Val(X) = {x1,…,xN} A distribution P(X | A) A utility function U(X, A)

Expected Utility Want to choose action a that maximizes the expected utility

Simple Influence Diagram 0.3 0.5 m1 m0 0.2 m2 Market Found U f1 f0 -7 m0 20 m2 5 m1

More Complex Influence Diagram Difficulty Intelligence Study Grade VG Letter VQ Job VS

Information Edges Market Survey Found Decision rule  at 0.3 0.5 m1 m0 0.2 m2 Market 0.1 0.3 0.6 m0 0.4 m2 m1 0.5 s0 s1 s2 Survey Found Decision rule  at action node A is a CPD: P(A | Parents(A)) f1 f0 -7 m0 20 m2 5 m1 U

Expected Utility with Information Want to choose the decision rule A that maximizes the expected utility

Finding MEU Decision Rules Market Survey Found U

Finding MEU Decision Rules Market Survey 0.1 0.3 0.6 m0 0.4 m2 m1 0.5 s0 s1 s2 f1 f0 -7 m0 20 m2 5 m1 0.3 0.5 m1 m0 0.2 m2 Found f1 f0 -1.25 s0 2.1 s2 1.15 s1 U

More Generally

MEU Algorithm Summary To compute MEU & optimize decision at A: Treat A as random variable with arbitrary CPD Introduce utility factor with scope PaU Eliminate all variables except A, Z (A’s parents) to produce factor (A, Z) For each z, set:

Decision Making under Uncertainty MEU principle provides rigorous foundation PGMs provide structured representation for probabilities, actions, and utilities PGM inference methods (VE) can be used for Finding the optimal strategy Determining overall value of the decision situation Efficient methods also exist for: Multiple utility components Multiple decisions

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