Utility Theory is the formal framework for representing an agent’s preferences over outcomes as a numerical utility function, such that the agent’s rational behaviour can be modelled as the maximisation of expected utility. It provides the axiomatic foundation — completeness, transitivity, continuity, and independence — under which preferences admit a utility representation. In artificial intelligence it grounds rational-agent design, decision-making under uncertainty, and the objective functions of planning and reinforcement-learning systems. It is closely tied to decision theory, game theory, and economic models of choice.
Overview
- Utility theory answers a foundational question: when can preferences over outcomes be represented by a single number such that preferring more utility is equivalent to preferring the outcome? The von Neumann-Morgenstern axioms give the answer for choice under risk.
- Expected utility maximisation provides the normative standard for rational decision-making under uncertainty, combining a utility function over outcomes with a probability distribution over states.
- In AI, utility functions define the objectives of rational agents, the reward structure of reinforcement learning, and the payoffs in game-theoretic and multi-agent settings.
Key aspects
- Axioms: completeness, transitivity, continuity, and independence guarantee a utility representation of preferences.
- Expected utility: the weighted average of outcome utilities under a probability distribution, maximised by rational agents.
- Risk attitudes: concavity and convexity of the utility function encode risk aversion and risk seeking.
- Descriptive limits: behavioural economics documents systematic deviations from expected-utility predictions, motivating prospect theory.
Applications
- Defining objective and reward functions for AI planning and reinforcement-learning agents.
- Modelling payoffs in game-theoretic analysis of multi-agent systems.
- Decision support and economic modelling of choice under risk.