# Distributionally Robust Optimization: A Review

arXiv: https://arxiv.org/abs/1908.05659 · HTML: https://mlsanity.com/paper/1908.05659/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2019.

## Built on by (most cited first, 30 of 76)

- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules](https://mlsanity.com/paper/2404.01245/) (2024)
- [Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertainty](https://mlsanity.com/paper/2404.18909/) (2024)
- [Adversarial Rademacher Complexity of Deep Neural Networks](https://mlsanity.com/paper/2211.14966/) (2022)
- [A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptation](https://mlsanity.com/paper/2410.19265/) (2024)
- [Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges](https://mlsanity.com/paper/2507.19672/) (2025)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysis](https://mlsanity.com/paper/2209.10825/) (2022)
- [Robustness in Large Language Models: A Survey of Mitigation Strategies and Evaluation Metrics](https://mlsanity.com/paper/2505.18658/) (2025)
- [Group Distributionally Robust Optimization-Driven Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2601.19280/) (2026)
- [A New Linear Scaling Rule for Private Adaptive Hyperparameter Optimization](https://mlsanity.com/paper/2212.04486/) (2022)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Worst-case generation via minimax optimization in Wasserstein space](https://mlsanity.com/paper/2512.08176/) (2025)
- [Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificity](https://mlsanity.com/paper/2301.13565/) (2023)
- [Efficient Stochastic Approximation of Minimax Excess Risk Optimization](https://mlsanity.com/paper/2306.00026/) (2023)
- [Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysis](https://mlsanity.com/paper/2307.14364/) (2023)
- [Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flows](https://mlsanity.com/paper/2407.11901/) (2024)
- [DEXTER: Diffusion-Guided EXplanations with TExtual Reasoning for Vision Models](https://mlsanity.com/paper/2510.14741/) (2025)
- [Variations on the Expectation due to Changes in the Probability Measure](https://mlsanity.com/paper/2502.02887/) (2025)
- [Proximal optimal transport divergences](https://mlsanity.com/paper/2505.12097/) (2025)
- [Causality-Inspired Robustness for Nonlinear Models via Representation Learning](https://mlsanity.com/paper/2505.12868/) (2025)
- [Conformalized Decision Risk Assessment](https://mlsanity.com/paper/2505.13243/) (2025)
- [Learning where to learn: Training data distribution optimization for scientific machine learning](https://mlsanity.com/paper/2505.21626/) (2025)
- [Distributionally robust minimization in meta-learning for system identification](https://mlsanity.com/paper/2506.18074/) (2025)
- [Property Elicitation on Imprecise Probabilities](https://mlsanity.com/paper/2507.05857/) (2025)
- [Distributionally Robust Optimal Power Flow with Contextual Information](https://mlsanity.com/paper/2109.07896/) (2021)
- [Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivity](https://mlsanity.com/paper/2208.03066/) (2022)
- [Distributional Robustness Bounds Generalization Errors](https://mlsanity.com/paper/2212.09962/) (2022)
- [Statistical Learning under Heterogeneous Distribution Shift](https://mlsanity.com/paper/2302.13934/) (2023)
- [Optimal Transport Regularized Divergences: Application to Adversarial Robustness](https://mlsanity.com/paper/2309.03791/) (2023)

## Abstract (arXiv)

The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization.