Jose Blanchet, Karthyek Murthy, Viet Anh Nguyen (2021) Statistical Analysis of Wasserstein Distributionally Robust Estimators. INFORMS TutORials in Operations Research null(null):227-254. https://doi.org/10.1287/educ.2021.0233
Abstract
We consider statistical methods that invoke a min-max distributionally robust formulation to extract good out-of-sample performance in data-driven optimization and learning problems. Acknowledging the distributional uncertainty in learning from limited samples, the min-max formulations introduce an adversarial inner player to explore unseen covariate data. The resulting distributionally robust optimization (DRO) formulations, which include Wasserstein DRO formulations (our main focus), are specified using optimal transportation phenomena. Upon describing how these infinite-dimensional min-max problems can be approached via a finite-dimensional dual reformulation, this tutorial moves into its main component, namely, explaining a generic recipe for optimally selecting the size of the adversary’s budget. This is achieved by studying the limit behavior of an optimal transport projection formulation arising from an …
Authors
Jose Blanchet, Karthyek Murthy, Viet Anh Nguyen
Publication date
2021/10
Book
Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications
Pages
227-254
Publisher
INFORMS
