Learning from Stochastically Revealed Preference

TL;DR

This paper addresses the challenge of learning the distribution of agents' utility functions from observed stochastic actions, proposing Bayesian methods for parameter estimation in Gaussian and corrupted utility settings.

Contribution

It introduces Bayesian approaches for inferring utility distributions in stochastic revealed preference scenarios, with theoretical guarantees and practical algorithms.

Findings

Bayesian methods effectively recover utility distribution parameters.

The algorithms perform well in Gaussian and corrupted utility settings.

Theoretical guarantees support the accuracy of parameter estimation.

Abstract

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.