Section 1 : Utility functions and decision networks

Commentary

Section Goals

• To introduce utility theory, functions, preference structure, and information value theory, which form the basis of decision-making techniques and decision-theoretic agents.
• To present decision networks, also known as influence diagrams, and their algorithms.

Learning Objectives

Learning Objective 1

• Explain the principle of maximum expected utility (MEU), and represent it with a formula.
• Describe the constraints on rational preferences, such as orderability, transitivity, continuity, substitutability, monotonicity, and decomposability.
• Describe utility function in the context of money and economy.
• Explain preference structures with or without uncertainty.
• Explain the mechanism, structure, and algorithm of decision-making.
• Describe an information-gathering agent based on the value of perfect information.
• Explain the following concepts or terms:
  • Preference
  • Utility function
  • Multiattribute utility theory
  • Preference independence
  • Utility independence
  • Mutual utility independence (MUI)
  • Influence diagram
  • Decision network
  • Value of perfect information
  • Information-gathering agent

Objective Readings

Required readings:

Reading topics:

Utility Theory, Utility Function, Decision Networks and the Value of Information (see Chapter 16 of AIMA3ed).

Supplemental Readings

Kjaerulff, U. B., and Madsen, A. L. (2008). Bayesian networks and influence diagrams: A guide to construction and analysis. Springer.

Garcia, L., and Sabbadin, R. (2008). Complexity results and algorithms for possibilistic influence diagrams. Artificial Intelligence, 172(8-9), 1018-1044.

Objective Questions

• How are preference and utility related?
• Why is information value theory useful for a decision-theoretic agent?

Objective Activities

• Explore utility theory in the context of economics to see if there are any new advancements that can be borrowed from the AI decision-making technique.
• Explore some open source or commercial decision-making software from the Web, and discuss them in the course conference.
• Have a look at a case study on decision-making expert systems by exploring the Web or the AU Digital Library resources.
• Complete Exercise 16.3 of AIMA3ed.
• Complete Exercise 16.17 of AIMA3ed.