Learning Economic Parameters from Revealed Preferences

Maria-Florina Balcan, Amit Daniely, Ruta Mehta, Ruth Urner, Vijay V. Vazirani

Abstract: A recent line of work, starting with Beigman and Vohra [4] and Zadimoghaddam and Roth [30], has addressed the problem of learning a utility function from revealed preference data. The goal here is to make use of past data describing the purchases of a utility maximizing agent when faced with certain prices and budget constraints in order to produce a hypothesis function that can accurately forecast the future behavior of the agent. In this work we advance this line of work by providing sample complexity guarantees and efficient algorithms for a number of important classes. By drawing a connection to recent advances in multi-class learning, we provide a computationally efficient algorithm with tight sample complexity guarantees ( $\tilde{\Theta}(d/\epsilon)$ for the case of d goods) for learning linear utility functions under a linear price model. This solves an open question in Zadimoghaddam and Roth [30]. Our technique yields numerous generalizations including the ability to learn other well-studied classes of utility functions, to deal with a misspecified model, and with non-linear prices.