# Recovering Best Statistical Guarantees via the Empirical Divergence-based Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/1605.09349 · HTML: https://mlsanity.com/paper/1605.09349/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2016.

## Built on by (most cited first, 30 of 33)

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- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Certified Robust Neural Networks: Generalization and Corruption Resistance](https://mlsanity.com/paper/2303.02251/) (2023)
- [Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimization](https://mlsanity.com/paper/2106.11180/) (2021)
- [Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions](https://mlsanity.com/paper/2207.04771/) (2022)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Learning and Decision-Making with Data: Optimal Formulations and Phase Transitions](https://mlsanity.com/paper/2109.06911/) (2021)
- [Smoothed f-Divergence Distributionally Robust Optimization](https://mlsanity.com/paper/2306.14041/) (2023)
- [Distributionally Robust Performative Prediction](https://mlsanity.com/paper/2412.04346/) (2024)
- [Stochastic Re-weighted Gradient Descent via Distributionally Robust Optimization](https://mlsanity.com/paper/2306.09222/) (2023)
- [Estimation Beyond Data Reweighting: Kernel Method of Moments](https://mlsanity.com/paper/2305.10898/) (2023)
- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [A data-driven approach to beating SAA out-of-sample](https://mlsanity.com/paper/2105.12342/) (2021)
- [Nested Stochastic Algorithm for Generalized Sinkhorn distance-Regularized Distributionally Robust Optimization](https://mlsanity.com/paper/2503.22923/) (2025)
- [Model Uncertainty and Correctability for Directed Graphical Models](https://mlsanity.com/paper/2107.08179/) (2021)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)
- [Efficient Data-Driven Optimization with Noisy Data](https://mlsanity.com/paper/2102.04363/) (2021)
- [Optimal Confidence Intervals via Moderate Deviations Theory](https://mlsanity.com/paper/2305.14496/) (2023)
- [Geometry-Aware Instrumental Variable Regression](https://mlsanity.com/paper/2405.11633/) (2024)
- [From Distributional Robustness to Robust Statistics: A Confidence Sets Perspective](https://mlsanity.com/paper/2410.14008/) (2024)
- [Calibrated Data-Dependent Constraints with Exact Satisfaction Guarantees](https://mlsanity.com/paper/2301.06195/) (2023)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)
- [Distributionally Robust Skeleton Learning of Discrete Bayesian Networks](https://mlsanity.com/paper/2311.06117/) (2023)
- [Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2503.04315/) (2025)

## Abstract (arXiv)

We investigate the use of distributionally robust optimization (DRO) as a tractable tool to recover the asymptotic statistical guarantees provided by the Central Limit Theorem, for maintaining the feasibility of an expected value constraint under ambiguous probability distributions. We show that using empirically defined Burg-entropy divergence balls to construct the DRO can attain such guarantees. These balls, however, are not reasoned from the standard data-driven DRO framework since by themselves they can have low or even zero probability of covering the true distribution. Rather, their superior statistical performances are endowed by linking the resulting DRO with empirical likelihood and empirical processes. We show that the sizes of these balls can be optimally calibrated using chi-square process excursion. We conduct numerical experiments to support our theoretical findings.