1. Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

2. Daphne Koller Utilities and Preferences 0.8 0.2 $4mil $0 0.75 0.25 $3mil $0

3. Daphne Koller Utility = Payoff 0.2 0.8 $4mil $0 0 1 $3mil $0

4. Daphne Koller Fair coin is tossed repeatedly until it comes up heads, say on the n th toss Payoff = $2 n St. Petersburg Paradox

5. Daphne Koller $ U Typical Utility Curve

6. Daphne Koller $ reward U 1000 0 500 UDUD 400 Certainty equivalent insurance/risk premium U($500) D= $0 with prob. 0.5 $1000 with prob. 0.5

7. Daphne Koller Multi-Attribute Utilities All attributes affecting preferences must be integrated into one utility function Human life – Micromorts – QALY (quality-adjusted life year)

8. Daphne Koller TestingKnowledge Loss of fetus Future pregnancy Down’s syndrome Example: Prenatal diagnosis U 1 (T) + U 2 (K) + U 3 (D,L) + U 4 (L,F)

9. Daphne Koller Summary Our utility function determines our preferences about decisions that involve uncertainty Utility generally depends on multiple factors – Money, time, chances of death, … Relationship is usually nonlinear – Shape of utility curve determines attitude to risk Multi-attribute utilities can help decompose high-dimensional function into tractable pieces

10. Daphne Koller END END END