Learning Economic Parameters from Revealed Preferences

A recent line of work, starting with Beigman and Vohra (2006) and Zadimoghaddam and Roth (2012), has addressed the problem of em 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 em 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 (Theta(d/ε) 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 (2012). 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.