Expected Utility

3203. Introduction to Artificial Intelligence

Decision and Expected Utility

When facing uncertainty, from "what to believe" to "which action to take".

Decision Theory studies how to behave rationally under uncertainty.

According to the classical model, a decision is a choice among alternative actions, according to their expected consequences.

Key notions:

action: a finite list
outcome: a finite list
preference: a relation over outcomes, include weakly/strictly preferred and indifferent
lottery: a probability distribution over outcomes, can be compared as an outcome in preference

Axioms of rational choices:

Completeness: An agent has preferences between all pairs of outcomes.
Transitivity: Preferences are transitive.
Monotonicity: An agent prefers a larger chance of getting a better outcome than a smaller chance of getting the same outcome.
Decomposability: An agent is indifferent between lotteries that have the same probabilities over the same outcomes.
Continuity: Preferences are continuous measurements.
Substitutability: Outcomes can be substituted while keeping preference.

An agent is defined to be rational if it obeys the above axioms.

Utility: a numerical measurement of preference, and utilities are linear with probabilities.

Decision theory is applied to intelligent agents under the following assumptions:

Agents know what actions they can carry out.
The effect of each action can be described as a probability distribution over outcomes.
An agent’s preferences are expressed by utilities of outcomes.

Under these conditions, an optimal single decision is the decision whose expected utility is maximal.