Outline Utilities and Decisions( Chap 22) Maximum Expected Utility(MEU) principle a Utility theor o Structured decision problems( Chap 23 a Decision tree a Influence diagrams MLA 2011, Tsinghua University
Outline Utilities and Decisions (Chap 22) ❑ Maximum Expected Utility (MEU) principle ❑ Utility theory Structured decision problems (Chap 23) ❑ Decision tree ❑ Influence diagrams 6 MLA 2011, Tsinghua University
Decision-making Situation o A decision-making situation D consists of et of outcomes o-f ON a a set of possible actions that an agent can take A=fal,.,aKJ a a probabilistic outcome model p: A-A0, which defines a lottery Ta Utility function U: 0+R, where U(O) preference fo the outcome o (o1);…;oN:丌a(ON) a a probability distribution over outcomes given the action a was taken Preference ordering: T1 7 T2 if the agent prefers T1 丌1~丌2 if the agent is indifferent between丌iand丌2 MLA 2011, Tsinghua University Compound lottery
Decision-making Situation A decision-making situation consists of ❑ a set of outcomes ❑ a set of possible actions that an agent can take ❑ a probabilistic outcome model , which defines a lottery ❑ a utility function , where is the agent’s preference for the outcome Lottery ❑ a probability distribution over outcomes given the action a was taken ❑ Preference ordering: 7 MLA 2011, Tsinghua University Compound Lottery
Maximum Expected Utility (MEU Principle o The Meu principle asserts that, in a decision-making situation D we should choose the action a that maximizes the expected utility EUDd]=∑xa(oU MLA 2011, Tsinghua University
Maximum Expected Utility (MEU) Principle The MEU principleasserts that, in a decision-making situation , we should choose the action that maximizes the expected utility 8 MLA 2011, Tsinghua University
One state/One Action Example SO EU[S0]=100x0.2+50x0.7+70x0.1 20+35+7 A1 62 S1 0.2 0.7 0.1 100 70 MLA 2011, Tsinghua University
One State/One Action Example s0 s1 s2 s3 A1 0.2 0.7 0.1 100 50 70 EU[S0] = 100 x 0.2 + 50 x 0.7 + 70 x 0.1 = 20 + 35 + 7 = 62 9 MLA 2011, Tsinghua University
One state/Two Actions Example SO ElsO=62 EU2S0=74 euso=maxEUlSo,Eu2ISOB 74 Al A2 S2 S4 0.2 0.70.20.1 100 50 70 MLA 2011, Tsinghua University
One State/Two Actions Example s0 s1 s2 s3 A1 0.2 0.7 0.1 100 50 70 A2 s4 0.2 0.8 80 • EU1[S0] = 62 • EU2[S0] = 74 • EU[S0] = max{EU1[S0],EU2[S0]} = 74 10 MLA 2011, Tsinghua University