Maximum Expected Utility

Daphne Koller

Decision Making

MaximumExpectedUtility

ProbabilisticGraphicalModels

Acting

Daphne Koller

Simple Decision MakingA 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)

Daphne Koller

Expected Utility

• Want to choose action a that maximizes the expected utility

Daphne Koller

Simple Influence Diagram

Market Found

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Daphne Koller

IntelligenceDifficulty

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More Complex Influence Diagram

Daphne Koller

Survey

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Decision rule at action node A is a CPD: P(A | Parents(A))

Daphne Koller

Expected Utility with Information

• Want to choose the decision rule A that maximizes the expected utility

Daphne Koller

Survey

Market

Found

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Finding MEU Decision Rules

Daphne Koller

Survey

Market

Found

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Finding MEU Decision Rules

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Daphne Koller

More Generally

Daphne Koller

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:

Daphne Koller

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

Daphne Koller

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