Beyond IID: data-driven decision-making in heterogeneous environments
Authors: Omar Besbes, Will Ma, Omar Mouchtaki

In this work, we study data-driven decision-making and depart from the classical identically and independently distributed (i.i.d.) assumption.  We present a new framework in which  historical samples   are generated from unknown and different distributions, which we dub  \textit{heterogeneous environments}.  These distributions are assumed to lie in a heterogeneity ball with known radius and centered around the (also) unknown future (out-of-sample) distribution on which the performance of a decision will be evaluated. We quantify the asymptotic worst-case regret that is achievable by central data-driven policies such as Sample Average Approximation, but also by rate-optimal ones,   as a function of the radius of the heterogeneity ball. Our work shows that the type of achievable performance varies considerably across different combinations of problem classes and notions of heterogeneity. We demonstrate the versatility of our framework by comparing achievable guarantees for the heterogeneous version of widely studied  data-driven problems such as  pricing, ski-rental, and newsvendor. En route, we establish a new connection between data-driven decision-making and distributionally robust optimization.