Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting.
Transcript of Daphne Koller Decision Making Utility Functions Probabilistic Graphical Models Acting.
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)
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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
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