Advanced AI

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Advanced AI

• Rob Lass
• July 26, 2006

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Administrative

• WebCT Problems?
• Why arent homeworks graded!?
• Midterm next Wed (Aug. 2nd)

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Today

• Short Lecture
• Utility theory, not NLP
• Game time!

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Utility Theory

• (write equation on board)
• Lottery
• Rational agents maximize expected utility
• Do humans do this?

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Notation and Constraints

• (write notation on board)
• Properties
• Transitivity avoid irrational cycles
• Orderability agents must have a preference (and
  therefore know utility functions)
• Continuity indifference in actions for certain
  probabilities
• Substitutability if probabilities are the same,
  an agent behaves the same in different lotteries
• Monotonicity prefer lotteries with a higher
  probability for reaching the most desired state
• Decomposability two lotteries can be compressed
  into one.

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Utility

• Utility Principle If an agents preferences
  obey these constraints, some utility function
  exists.
• Maximum Expected Utility Principle Determine
  the utility of a lottery.

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Money

• Can it be substituted for a utility function?
• Question
• Would you prefer to have 1 million dollars, or
  3 million dollars?
• Pick one
• I will give you 1 million US dollars
• I will flip a fair coin, and give you 2,000,020
  if it is heads, and 0 if it is tails.
• Based on utility theory, which is the rational
  choice?

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Risk Assessment

• Pick
• 80 chance of 4000
• 100 chance of 3000
• Pick
• 20 chance of 4000
• 25 chance of 3000
• Page 592 describes a study of this. Summary
  people are risk averse with high probability
  events, and risk tolerant with low probability
  events.

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Life and Death

• What is the value of your life? (draw notation on
  board)
• Micromort 1/1,000,000 chance of death
• What is this worth to you?
• Studies have shown 20 / micromort
• Micromort Activities
• Swimming / 1 hr
• Skydiving / 0.5 seconds
• Flying (Commercial) / 7 hrs
• Bicycling / 4hrs
• Would you kill yourself for 20 million?

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Oh boy, its game time!
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• A) Number of passengers who flew between NY and
  LA in 1989
• B) Population of warsaw in 1992
• C) Year in which Coronado discovered the
  Mississippi River
• D) Number of votes received by Jimmy Carter in
  the 1976 prez election
• E) Age of the oldest living tree, in 2002
• F) Height of the Hoover Dam in ft
• G) Number of eggs produced in Oregon in 1985
• H) Number of Buddhists in the world in 1992
• I) Number of deaths due to AIDS in the US in 1981
• J) Number of US patents granted in 1901