Advanced AI

Rob Lass

July 26, 2006

Administrative

• WebCT Problems?

• Why aren’t homeworks graded!?

• Midterm next Wed (Aug. 2nd)

Today

• Short Lecture– Utility theory, not NLP

• Game time!

Utility Theory

• (write equation on board)

• Lottery

• Rational agents maximize expected utility;

• Do humans do this?

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.

Utility

• Utility Principle: If an agent’s preferences obey these constraints, some utility function exists.

• Maximum Expected Utility Principle: Determine the utility of a lottery.

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?

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.

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?

Oh boy, it’s game time!

• 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