Statistical Limit Theorems in Distributionally Robust Optimization
Optimization and Control
2023-03-28 v1 Statistics Theory
Statistics Theory
Abstract
The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various settings, including both phi-divergence and Wasserstein uncertainty sets. Different types of asymptotic behaviors are obtained depending on the rate at which the uncertainty radius decreases to zero as a function of the sample size and the geometry of the uncertainty sets.
Cite
@article{arxiv.2303.14867,
title = {Statistical Limit Theorems in Distributionally Robust Optimization},
author = {Jose Blanchet and Alexander Shapiro},
journal= {arXiv preprint arXiv:2303.14867},
year = {2023}
}