# Statistical Limit Theorems in Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2303.14867 · HTML: https://mlsanity.com/paper/2303.14867/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2023.

## Built on by (most cited first, 7 of 7)

- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Sets](https://mlsanity.com/paper/2403.14822/) (2024)
- [Distributionally robust risk evaluation with an isotonic constraint](https://mlsanity.com/paper/2407.06867/) (2024)
- [Optimal Confidence Intervals via Moderate Deviations Theory](https://mlsanity.com/paper/2305.14496/) (2023)
- [Asymptotic Behavior of Adversarial Training Estimator under ℓ_∞-Perturbation](https://mlsanity.com/paper/2401.15262/) (2024)
- [From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective](https://mlsanity.com/paper/2410.14008/) (2024)

## Abstract (arXiv)

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.