  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.
