Graphical Models for Preference and Utility

TL;DR

This paper explores how graphical models and independence concepts can simplify the elicitation, representation, and computation of utility functions in multi-attribute decision-making, introducing new theoretical insights.

Contribution

It introduces the concept of conditional additive independence for utility functions and shows its representation as a Markov network, linking utility decomposition to graphical models.

Findings

Conditional additive independence always has a perfect Markov network representation.

The utility function's decomposition speeds up expected utility calculations.

The approach connects utility functions with probabilistic graphical models.

Abstract

Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing notions of independence for utility functions in a multi-attribute space, and suggest that these can be used to achieve similar advantages. Our new results concern conditional additive independence, which we show always has a perfect representation as separation in an undirected graph (a Markov network). Conditional additive independencies entail a particular functional for the utility function that is analogous to a product decomposition of a probability function, and confers analogous benefits. This functional form has been utilized in the Bayesian network and influence diagram literature, but generally without an explanation in terms of independence. The functional form yields a decomposition of the utility function that can greatly speed up expected utility calculations, particularly when the utility graph has a similar topology to the probabilistic network being used.