Assume time money cost of taking highway to work wo

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Unformatted text preview:   We’d like to define uHlity funcHons over variables in some clever way •  What’s a natural way to decompose uHlity? 8 AddiHve Independence •  •  •  •  •  •  •  Suppose it makes me happy to have my car clean Suppose it makes me happy to have coffee U=U(coffee)+U(clean) It seems that these don’t interact However, suppose there’s a tea variable U=U(coffee)+U(tea)+U(clean)??? Probably not. I’d need U(coffee,tea)+U(clean) •  Parallel theory to decomposiHon of uHliHes into state variables as with Bayesian networks Value of InformaHon •  Expected uHlity of acHon a with evidence E: EUE ( A | E ) = max ∑ P( Si | E, a)U( Si ) a i •  Expected uHlity given new evidence E’ € EUE ,E + ( A | E, E ' ) = max ∑ P( Si | E, E ', a)U( Si ) a i •  Value of knowing E’ (value of perfect informaHon) ȹ ȹ VPIE (E ) = ȹ ∑ P(E ' | E )EUE ,E + (a' | E, E ' )ȹ − EU(a | E ) + € ȹ E + Ⱥ Previous Expected uHlity given Expected New informaHon uHlity (weighted) € 9 VPI Example •  Should you pay to subscribe for tra...
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This note was uploaded on 02/17/2012 for the course COMPSCI 170 taught by Professor Parr during the Spring '11 term at Duke.

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