Efficiently Learning from Revealed Preference

TL;DR

This paper presents efficient algorithms for learning utility functions from revealed preferences, enabling accurate future behavior prediction for agents with linear and certain concave valuations, with polynomial sample complexity.

Contribution

It introduces novel polynomial-sample algorithms for learning utility functions from revealed preferences, covering linear and linearly separable concave cases.

Findings

Algorithms achieve polynomial sample complexity.

Effective for linear valuation functions.

Applicable to linearly separable, concave valuation functions.

Abstract

In this paper, we consider the revealed preferences problem from a learning perspective. Every day, a price vector and a budget is drawn from an unknown distribution, and a rational agent buys his most preferred bundle according to some unknown utility function, subject to the given prices and budget constraint. We wish not only to find a utility function which rationalizes a finite set of observations, but to produce a hypothesis valuation function which accurately predicts the behavior of the agent in the future. We give efficient algorithms with polynomial sample-complexity for agents with linear valuation functions, as well as for agents with linearly separable, concave valuation functions with bounded second derivative.