# Distributionally Robust Optimization and Robust Statistics

arXiv: https://arxiv.org/abs/2401.14655 · HTML: https://mlsanity.com/paper/2401.14655/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2024.

## Built on by (most cited first, 24 of 24)

- [DRO: A Python Library for Distributionally Robust Optimization in Machine Learning](https://mlsanity.com/paper/2505.23565/) (2025)
- [textttskwdro: a library for Wasserstein distributionally robust machine learning](https://mlsanity.com/paper/2410.21231/) (2024)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (2024)
- [Learning a Single Neuron Robustly to Distributional Shifts and Adversarial Label Noise](https://mlsanity.com/paper/2411.06697/) (2024)
- [Wasserstein Distributionally Robust Regret Optimization](https://mlsanity.com/paper/2504.10796/) (2025)
- [Wasserstein-Cram'er-Rao Theory of Unbiased Estimation](https://mlsanity.com/paper/2511.07414/) (2025)
- [Automatic Outlier Rectification via Optimal Transport](https://mlsanity.com/paper/2403.14067/) (2024)
- [Stability Evaluation via Distributional Perturbation Analysis](https://mlsanity.com/paper/2405.03198/) (2024)
- [A Reliability Theory of Compromise Decisions for Large-Scale Stochastic Programs](https://mlsanity.com/paper/2405.10414/) (2024)
- [Epistemic Errors of Imperfect Multitask Learners When Distributions Shift](https://mlsanity.com/paper/2505.23496/) (2025)
- [A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2507.01932/) (2025)
- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)
- [Data Heterogeneity Modeling for Trustworthy Machine Learning](https://mlsanity.com/paper/2506.00969/) (2025)
- [Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2506.04948/) (2025)
- [Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Control](https://mlsanity.com/paper/2506.19294/) (2025)
- [Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric](https://mlsanity.com/paper/2509.04089/) (2025)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [A first-order method for constrained nonconvex-nonconcave minimax optimization](https://mlsanity.com/paper/2510.01168/) (2025)
- [Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination](https://mlsanity.com/paper/2601.11420/) (2026)
- [A Causal Framework for Mitigating Data Shifts in Healthcare](https://mlsanity.com/paper/2603.13595/) (2026)
- [On the Stability and Generalization of First-order Bilevel Minimax Optimization](https://mlsanity.com/paper/2604.20115/) (2026)
- [Unification and Optimization of Robust Supervised Learning](https://mlsanity.com/paper/2605.28165/) (2026)
- [Conservative neural posterior estimation via distributionally robust training](https://mlsanity.com/paper/2605.28516/) (2026)
- [A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems](https://mlsanity.com/paper/2606.30230/) (2026)

## Abstract (arXiv)

We review distributionally robust optimization (DRO), a principled approach for constructing statistical estimators that hedge against the impact of deviations in the expected loss between the training and deployment environments. Many well-known estimators in statistics and machine learning (e.g. AdaBoost, LASSO, ridge regression, dropout training, etc.) are distributionally robust in a precise sense. We hope that by discussing the DRO interpretation of well-known estimators, statisticians who may not be too familiar with DRO may find a way to access the DRO literature through the bridge between classical results and their DRO equivalent formulation. On the other hand, the topic of robustness in statistics has a rich tradition associated with removing the impact of contamination. Thus, another objective of this paper is to clarify the difference between DRO and classical statistical robustness. As we will see, these are two fundamentally different philosophies leading to completely different types of estimators. In DRO, the statistician hedges against an environment shift that occurs after the decision is made; thus DRO estimators tend to be pessimistic in an adversarial setting, leading to a min-max type formulation. In classical robust statistics, the statistician seeks to correct contamination that occurred before a decision is made; thus robust statistical estimators tend to be optimistic leading to a min-min type formulation.