Daphne Koller

U"lity  Func"ons  

Probabilis"c  Graphical  Models   Decision  Making  

Ac"ng  

Utilities and Preferencesf

0.2 $4mil 0.25 $3milf

p

0.8 $0 0.75 $0≈

Daphne Koller

Utility = Payoff?y y ff

0.8 $4mil 1 $3milf

p

0.2 $0 0 $0≈

Daphne Koller

St. Petersburg Paradox• Fair coin is tossed repeatedly until it

gp y

comes up heads, say on the nth toss• Payoff = $2n• Payoff = $2n

Daphne Koller

UU($500)

UD

U($500)D=

$0 with prob. 1-p

$1000 with prob pUD $1000 with prob. p

$ reward10000 500400

C t i t i l t

Daphne Koller

Certainty equivalent insurance/risk premium

Typical Utility CurveU

yp yU

$

Daphne Koller

Multi-Attribute Utilities• All attributes affecting preferences must g p

be integrated into one utility function

H l f• Human life– Micromorts

Daphne Koller

– QALY (quality-adjusted life year)

Example: Prenatal diagnosismp gU1(T) + U2(K) + U3(D,L) + U4(L,F)

Testing Knowledgeg g

f’ Loss offetus

Futurepregnancy

Down’ssyndrome

Daphne Koller

Summarymm y• Our utility function determines our preferences

b t d isi s th t i l t i tabout decisions that involve uncertainty• Utility generally depends on multiple factors

M ti h f d th – Money, time, chances of death, …• Relationship is usually nonlinear

Sh f tilit d t i ttit d t i k– Shape of utility curve determines attitude to risk• Multi-attribute utilities can help decompose

high dimensional function into tractable pieces

Daphne Koller

high-dimensional function into tractable pieces