Statistical Limit Theorems in Distributionally Robust Optimization

Jose Blanchet; Alexander Shapiro

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arXiv · 2303.14867

Statistical Limit Theorems in Distributionally Robust Optimization

Jose Blanchet·Alexander Shapiro

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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.

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Jose Blanchet, Alexander Shapiro. 2023-03-27. Statistical Limit Theorems in Distributionally Robust Optimization. https://arxiv.org/abs/2303.14867

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