Technical Note—Dynamic Data-Driven Estimation of Nonparametric Choice Models

Abstract

Choice models are prevalent in several application areas, and their nonparametric estimation was introduced to alleviate unreasonable assumptions in traditional parametric models. Existing literature focuses only on the static observational setting where all of the observations are given up front and lacks algorithms that provide explicit convergence rate guarantees or an a priori analysis for the model accuracy versus sparsity trade-off on the actual estimated model returned. In contrast, in “Dynamic Data-Driven Estimation of Nonparametric Choice Models,” Ho-Nguyen and Kılınç-Karzan focus on estimating a nonparametric choice model from observational data in a dynamic setting, where observations are obtained over time. They show that this estimation problem can be cast as a convex-concave saddle point joint estimation and optimization problem and provide an online convex optimization-based primal-dual framework for deriving algorithms for it. By tailoring this framework carefully to the choice model estimation problem, they provide low-cost algorithms that come with provable convergence guarantees, explicit theoretical bounds on the sparsity of the estimated model, and a superior empirical performance.