  We study the learning problem of revealed preference in a stochastic setting:
a learner observes the utility-maximizing actions of a set of agents whose
utility follows some unknown distribution, and the learner aims to infer the
distribution through the observations of actions. The problem can be viewed as
a single-constraint special case of the inverse linear optimization problem.
Existing works all assume that all the agents share one common utility which
can easily be violated under practical contexts. In this paper, we consider two
settings for the underlying utility distribution: a Gaussian setting where the
customer utility follows the von Mises-Fisher distribution, and a
$\delta$-corruption setting where the customer utility distribution
concentrates on one fixed vector with high probability and is arbitrarily
corrupted otherwise. We devise Bayesian approaches for parameter estimation and
develop theoretical guarantees for the recovery of the true parameter. We
illustrate the algorithm performance through numerical experiments.
