Feature Misspecification in Sequential Learning Problems

Abstract

We consider a class of sequential learning problems where a decision maker must learn the unknown statistical characteristics of a finite set of alternatives (or systems) using sequential sampling to ultimately select a subset of “good” alternatives. A salient feature of our problem is that system performance is governed by a set of features. The decision maker postulates the dependence on these features to be linear, but this model may not precisely represent the true underlying system structure. We show that this misspecification, if not managed properly, can lead to suboptimal performance because of a phenomenon identified as sample-selection endogeneity. We propose a prospective sampling principle—a new approach that eliminates the adverse effects of misspecification as the number of samples grows large. The proposed principle applies across a very general class of widely used sampling policies, enjoys strong asymptotic performance guarantees, and exhibits effective finite-sample performance in numerical experiments. This paper was accepted by Vivek Farias, data science. Funding: This work was supported by the United States-Israel Binational Science Foundation [Grant 2020063] and the Hong Kong Research Grant Council [GRF Grant 16501821 and ECS Grant 24210420]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.00328 .