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Distributionally Robust Optimization: A Review

arXiv 1908.05659 ↗First posted 13 Aug 2019math.OC cs.LG stat.MLcited by 76

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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.

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

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Citing papers per year: 2021: 2; 2022: 8; 2023: 10; 2024: 18; 2025: 20; 2026: 18.

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  1. 2023Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignmentcited by 401
  2. 2024A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rulescited by 57
  3. 2024Sample-Efficient Robust Multi-Agent Reinforcement Learning in the Face of Environmental Uncertaintycited by 25
  4. 2022Adversarial Rademacher Complexity of Deep Neural Networkscited by 18
  5. 2024A Survey of Deep Graph Learning under Distribution Shifts: from Graph Out-of-Distribution Generalization to Adaptationcited by 17
  6. 2025Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challengescited by 15
  7. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 13
  8. 2022Nonsmooth Nonconvex-Nonconcave Minimax Optimization: Primal-Dual Balancing and Iteration Complexity Analysiscited by 12
  9. 2025Robustness in Large Language Models: A Survey of Mitigation Strategies and Evaluation Metricscited by 12
  10. 2026Group Distributionally Robust Optimization-Driven Reinforcement Learning for LLM Reasoningcited by 12
  11. 2022A New Linear Scaling Rule for Private Adaptive Hyperparameter Optimizationcited by 11
  12. 2024Differentiable Distributionally Robust Optimization Layerscited by 8
38 more
  1. 2025Worst-case generation via minimax optimization in Wasserstein spacecited by 7
  2. 2023Learning Against Distributional Uncertainty: On the Trade-off Between Robustness and Specificitycited by 4
  3. 2023Efficient Stochastic Approximation of Minimax Excess Risk Optimizationcited by 4
  4. 2023Federated Distributionally Robust Optimization with Non-Convex Objectives: Algorithm and Analysiscited by 4
  5. 2024Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flowscited by 4
  6. 2025DEXTER: Diffusion-Guided EXplanations with TExtual Reasoning for Vision Modelscited by 4
  7. 2025Variations on the Expectation due to Changes in the Probability Measurecited by 3
  8. 2025Proximal optimal transport divergencescited by 3
  9. 2025Causality-Inspired Robustness for Nonlinear Models via Representation Learningcited by 3
  10. 2025Conformalized Decision Risk Assessmentcited by 3
  11. 2025Learning where to learn: Training data distribution optimization for scientific machine learningcited by 3
  12. 2025Distributionally robust minimization in meta-learning for system identificationcited by 3
  13. 2025Property Elicitation on Imprecise Probabilitiescited by 3
  14. 2021Distributionally Robust Optimal Power Flow with Contextual Informationcited by 2
  15. 2022Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivitycited by 2
  16. 2022Distributional Robustness Bounds Generalization Errorscited by 2
  17. 2023Statistical Learning under Heterogeneous Distribution Shiftcited by 2
  18. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  19. 2024An Inexact Halpern Iteration with Application to Distributionally Robust Optimizationcited by 2
  20. 2024Operationalizing the Blueprint for an AI Bill of Rights: Recommendations for Practitioners, Researchers, and Policy Makerscited by 2
  21. 2024Learning Randomized Algorithms with Transformerscited by 2
  22. 2024Revisiting Extragradient-Type Methods -- Part 1: Generalizations and Sublinear Convergence Ratescited by 2
  23. 2024Learning a Single Neuron Robustly to Distributional Shifts and Adversarial Label Noisecited by 2
  24. 2024Causal Invariance Learning via Efficient Nonconvex Optimizationcited by 2
  25. 2025Group Distributionally Robust Optimization with Flexible Sample Queriescited by 2
  26. 2025Lightweight Robust Direct Preference Optimizationcited by 2
  27. 2026VQ-Seg: Vector-Quantized Token Perturbation for Semi-Supervised Medical Image Segmentationcited by 2
  28. 2026Reasoning Is Not Free: Robust Adaptive Cost-Efficient Routing for LLM-as-a-Judgecited by 2
  29. 2023A Robust Twin Parametric Margin Support Vector Machine for Multiclass Classificationcited by 1
  30. 2024Bayesian Nonparametrics Meets Data-Driven Distributionally Robust Optimizationcited by 1
  31. 2024Stability Evaluation via Distributional Perturbation Analysiscited by 1
  32. 2024Optimal Transport for Probabilistic Circuitscited by 1
  33. 2024On Calibration in Multi-Distribution Learningcited by 1
  34. 2025A first-order method for nonconvex-nonconcave minimax problems under a local Kurdyka-Lojasiewicz conditioncited by 1
  35. 2026Shapes are not enough: CONSERVAttack and its use for finding vulnerabilities and uncertainties in machine learning applicationscited by 1
  36. 2026Distributionally Robust PAC-Bayesian Controlcited by 1
  37. 2026Generalized Neural Operator for Parametric and Boundary-Value Problemscited by 1
  38. 2026Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Setcited by 1

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