# Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2411.02549 · HTML: https://mlsanity.com/paper/2411.02549/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 85 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Data-Driven Robust Optimization](https://mlsanity.com/paper/1401.0212/) (2013)
- [On Distributionally Robust Chance Constrained Programs with Wasserstein Distance](https://mlsanity.com/paper/1806.07418/) (2018)
- [Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls](https://mlsanity.com/paper/1609.07505/) (2016)

## Built on by (most cited first, 1 of 1)

- [Achieving First-Order Statistical Improvements in Data-Driven Optimization: From No-Free-Lunch to Amplified Decision Perturbation](https://mlsanity.com/paper/2608.04312/) (2026)

## Abstract (arXiv)

Distributionally robust optimization (DRO) studies decision problems under uncertainty where the probability distribution governing the uncertain problem parameters is itself uncertain. A key component of any DRO model is its ambiguity set, that is, a family of probability distributions consistent with any available structural or statistical information. DRO seeks decisions that perform best under the worst distribution in the ambiguity set. This worst case criterion is supported by findings in psychology and neuroscience, which indicate that many decision-makers have a low tolerance for distributional ambiguity. DRO is rooted in statistics, operations research and control theory, and recent research has uncovered its deep connections to regularization techniques and adversarial training in machine learning. This survey presents the key findings of the field in a unified and self-contained manner.