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Unformatted text preview: Decision Theory CPS 170 Ronald Parr Decision Theory What does it mean to make an opHmal decision? •  •  •  •  •  Asked by economists to study consumer behavior Asked by MBAs to maximize profit Asked by leaders to allocate resources Asked in OR to maximize efficiency of operaHons Asked in AI to model intelligence •  Asked (sort of) by any intelligent person every day 1 UHlity FuncHons •  A u"lity func"on is a mapping from world states to real numbers •  SomeHmes called a value func"on •  RaHonal or opHmal behavior is typically viewed as maximizing expected uHlity: max ∑ P( s | a)U( s) a s a = acHons, s = states € Are UHlity FuncHons Natural? •  Some have argued that people don’t really have uHlity funcHons •  What is the uHlity of the current state? •  What was your uHlity at 8:00pm last night? •  U"lity elicita"on is difficult problem •  It’s easy to communicate preferences •  Theorem (sorta): Given a plausible set of assumpHons about your preferences, there must exist a consistent uHlity funcHon 2 Axioms of UHlity Theory •  Orderability: ( A B) ∨ ( A B) ∨ ( A ~ B...
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