Lecture 16: Making Simple Decisions

Lecture 16: Making Simple Decisions¶

AIMA Chapter 16 — 1 hour¶

Why Decision Theory Matters¶

• Combine probability and utility

• Rational action under uncertainty

• Medical diagnosis and treatment

• Business decisions, robotics, games

Learning Objectives¶

• Combine beliefs and desires (utility theory)

• Apply expected utility maximization

• Use decision networks

• Compute value of information

Utility Theory¶

• Preferences: A ≻ B (prefer A to B)

• Axioms: Orderability, transitivity, etc.

• Theorem: Rational preferences → utility function exists

Expected Utility¶

• EU(A) = Σₛ P(s|a) U(s)

• Principle: Maximize EU

• Lottery: Probability distribution over outcomes

Utility Functions¶

• Assessment: Standard gamble

• Money: Risk aversion (concave)

• Multiattribute: Combine utilities

Decision Networks¶

• Chance nodes: Random variables

• Decision nodes: Agent’s choices

• Utility node: Value

• Evaluate: For each decision, compute EU

Value of Information¶

• VPI: Expected improvement from observing

• VPI(E) = EU(with E) - EU(without E)

• Never negative

• Zero if E irrelevant

Summary¶

• Utility: Preferences → numbers

• EU: Maximize expected utility

• Decision networks: Evaluate decisions

• VPI: Value of information

References¶

• AIMA Ch. 16

• Russell & Norvig, AIMA 4e, Ch. 16

• Chapter PDF: chapters/chapter-16.pdf

Questions?¶

Next lecture: Making Complex Decisions (Chapter 17)