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Daphne Koller
Decision Making
UtilityFunctions
ProbabilisticGraphicalModels
Acting
Daphne Koller
Utilities and Preferences
0.8
0.2 $4mil
$0 0.75
0.25 $3mil
$0
Daphne Koller
Utility = Payoff
0.2
0.8 $4mil
$0 0
1 $3mil
$0
Daphne Koller
• Fair coin is tossed repeatedly until it comes up heads, say on the nth toss
• Payoff = $2n
St. Petersburg Paradox
Daphne Koller
$
U
Typical Utility Curve
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
Daphne Koller
Multi-Attribute Utilities• All attributes affecting preferences
must be integrated into one utility function
• Human life–Micromorts– QALY (quality-adjusted life year)
Daphne Koller
Testing Knowledge
Loss offetus
Futurepregnancy
Down’ssyndrome
Example: Prenatal diagnosisU1(T) + U2(K) + U3(D,L) + U4(L,F)
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
Daphne Koller
END END END