Nonparametric estimation of utility functions

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.