Nonparametric estimation of utility functions

TL;DR

This paper presents a Bayesian nonparametric approach using Gaussian processes for estimating utility functions, offering greater flexibility and improved accuracy over traditional parametric methods, with promising results for both single and multi-attribute cases.

Contribution

Introduces a novel Bayesian nonparametric method for utility function estimation using Gaussian processes, enhancing flexibility and theoretical properties.

Findings

Lower mean squared errors in estimates

Effective for single-attribute utility functions

Promising results for multi-attribute utility estimation

Abstract

Inferring a decision maker's utility function typically involves an elicitation phase where the decision maker responds to a series of elicitation queries, followed by an estimation phase where the state-of-the-art is to either fit the response data to a parametric form (such as the exponential or power function) or perform linear interpolation. We introduce a Bayesian nonparametric method involving Gaussian stochastic processes for estimating a utility function. Advantages include the flexibility to fit a large class of functions, favorable theoretical properties, and a fully probabilistic view of the decision maker's preference properties including risk attitude. Using extensive simulation experiments as well as two real datasets from the literature, we demonstrate that the proposed approach yields estimates with lower mean squared errors. While our focus is primarily on single-attribute utility functions, one of the real datasets involves three attributes; the results indicate that nonparametric methods also seem promising for multi-attribute utility function estimation.