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

2. 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)

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

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

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

6. 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

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

8. Finding MEU Decision Rules
Market
Survey
Found U

9. 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

10. More Generally

11. 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:

12. 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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