Utilities as Random Variables: Density Estimation and Structure Discovery

TL;DR

This paper introduces a Bayesian density estimation framework treating utility functions as random variables, enabling structure discovery and robust utility estimation with fewer questions in decision-making contexts.

Contribution

It presents a novel Bayesian approach to model utility functions as densities, allowing structure discovery and improved utility estimation from limited data.

Findings

Effective density estimation of utility functions from partial data

Discovery of utility function structures using Bayesian model selection

Robust utility estimates with fewer elicitation questions

Abstract

Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density function over its possible values. We show that we can apply statistical density estimation techniques to learn such a density function from a database of partially elicited utility functions. In particular, we define a Bayesian learning framework for this problem, assuming the distribution over utilities is a mixture of Gaussians, where the mixture components represent statistically coherent subpopulations. We can also extend our techniques to the problem of discovering generalized additivity structure in the utility functions in the population. We define a Bayesian model selection criterion for utility function structure and a search procedure over structures. The factorization of the utilities in the learned model, and the generalization obtained from density estimation, allows us to provide robust estimates of utilities using a significantly smaller number of utility elicitation questions. We experiment with our technique on synthetic utility data and on a real database of utility functions in the domain of prenatal diagnosis.