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Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

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Page 1: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

Decision Making

UtilityFunctions

ProbabilisticGraphicalModels

Acting

Page 2: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

Utilities and Preferences

0.8

0.2 $4mil

$0 0.75

0.25 $3mil

$0

Page 3: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

Utility = Payoff

0.2

0.8 $4mil

$0 0

1 $3mil

$0

Page 4: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

• Fair coin is tossed repeatedly until it comes up heads, say on the nth toss

• Payoff = $2n

St. Petersburg Paradox

Page 5: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

$

U

Typical Utility Curve

Page 6: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

$ reward

U

10000 500

UD

400

Certainty equivalent insurance/risk premium

U($500)

D=$0 with prob. 0.5

$1000 with prob. 0.5

Page 7: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

Multi-Attribute Utilities• All attributes affecting preferences

must be integrated into one utility function

• Human life–Micromorts– QALY (quality-adjusted life year)

Page 8: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

Testing Knowledge

Loss offetus

Futurepregnancy

Down’ssyndrome

Example: Prenatal diagnosisU1(T) + U2(K) + U3(D,L) + U4(L,F)

Page 9: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

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

Page 10: Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting

Daphne Koller

END END END


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