Learning underspecified models

Abstract

This paper examines learning dynamics under non-parametric model uncertainty. We choose the monopolistic profit maximization problem (Myerson (1981)) as our laboratory. We consider a monopolist who chooses a learning algorithm to select a price following a history, facing non-parametric model uncertainty about the probability distribution of the buyer's valuation and bearing the computational cost. We posit that the monopolist has a lexicographic preference over profit and computational complexity while seeking an ϵ dominant algorithm that prescribes an ϵ best response against any cumulative distribution function of the buyer's valuation for any small ϵ>0. We construct a simplest ϵ dominant algorithm among all dominant algorithms when the distribution of the buyer's valuation satisfies the increasing hazard rate property. Our algorithm recursively estimates two parameters of the distribution, even if the actual distribution is parameterized by many more variables. The monopolist chooses a misspecified model to save computational cost while learning the true optimal decision uniformly over the set of feasible distributions.