mlsanityData to 14 Oct 2026

Distributionally Robust Optimization and Generalization in Kernel Methods

arXiv 1905.10943 ↗First posted 27 May 2019cs.LG stat.MLcited by 73

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Abstract (arXiv)

Distributionally robust optimization (DRO) has attracted attention in machine learning due to its connections to regularization, generalization, and robustness. Existing work has considered uncertainty sets based on phi-divergences and Wasserstein distances, each of which have drawbacks. In this paper, we study DRO with uncertainty sets measured via maximum mean discrepancy (MMD). We show that MMD DRO is roughly equivalent to regularization by the Hilbert norm and, as a byproduct, reveal deep connections to classic results in statistical learning. In particular, we obtain an alternative proof of a generalization bound for Gaussian kernel ridge regression via a DRO lense. The proof also suggests a new regularizer. Our results apply beyond kernel methods: we derive a generically applicable approximation of MMD DRO, and show that it generalizes recent work on variance-based regularization.

Key facts. Cited by 73 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 May 2019.

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Citing papers per year: 2021: 14; 2022: 14; 2023: 19; 2024: 11; 2025: 8; 2026: 7.

73 papers.

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  1. 2023Diagnosing Model Performance Under Distribution Shiftcited by 39
  2. 2021Sinkhorn Distributionally Robust Optimizationcited by 38
  3. 2023Learning to Augment Distributions for Out-of-Distribution Detectioncited by 38
  4. 2021Regularized Policies are Reward Robustcited by 32
  5. 2022Minimax Regret Optimization for Robust Machine Learning under Distribution Shiftcited by 31
  6. 2023Not All Semantics are Created Equal: Contrastive Self-supervised Learning with Automatic Temperature Individualizationcited by 25
  7. 2022Near-Optimal Algorithms for Group Distributionally Robust Optimization and Beyondcited by 17
  8. 2022Distributionally Robust Bayesian Optimization with varphi-divergencescited by 16
  9. 2022Stochastic Constrained DRO with a Complexity Independent of Sample Sizecited by 16
  10. 2022Domain-Specific Risk Minimization for Out-of-Distribution Generalizationcited by 15
  11. 2024Score-based generative models are provably robust: an uncertainty quantification perspectivecited by 15
  12. 2021Poisoning Attack against Estimating from Pairwise Comparisonscited by 14
38 more
  1. 2021Algorithmic Bias and Data Bias: Understanding the Relation between Distributionally Robust Optimization and Data Curationcited by 13
  2. 2022Instance-Dependent Generalization Bounds via Optimal Transportcited by 13
  3. 2025Distributionally Robust Reinforcement Learning with Human Feedbackcited by 12
  4. 2021Generalization Bounds with Minimal Dependency on Hypothesis Class via Distributionally Robust Optimizationcited by 9
  5. 2022Minimax risk classifiers with 0-1 losscited by 9
  6. 2023Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Modelscited by 9
  7. 2023Moderately Distributional Exploration for Domain Generalizationcited by 8
  8. 2025Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiencycited by 8
  9. 2025Prompt Disentanglement via Language Guidance and Representation Alignment for Domain Generalizationcited by 8
  10. 2022Certifying Out-of-Domain Generalization for Blackbox Functionscited by 7
  11. 2022Online Kernel CUSUM for Change-Point Detectioncited by 7
  12. 2023Adversarial Constrained Bidding via Minimax Regret Optimization with Causality-Aware Reinforcement Learningcited by 7
  13. 2023Smoothed f-Divergence Distributionally Robust Optimizationcited by 7
  14. 2023Topology-aware Robust Optimization for Out-of-distribution Generalizationcited by 7
  15. 2024On the Benefits of Over-parameterization for Out-of-Distribution Generalizationcited by 7
  16. 2024Beyond the Federation: Topology-aware Federated Learning for Generalization to Unseen Clientscited by 7
  17. 2021Robust Generalization despite Distribution Shift via Minimum Discriminating Informationcited by 6
  18. 2022Tikhonov Regularization is Optimal Transport Robust under Martingale Constraintscited by 6
  19. 2023Geometry-Calibrated DRO: Combating Over-Pessimism with Free Energy Implicationscited by 5
  20. 2024Evaluating Model Performance Under Worst-case Subpopulationscited by 5
  21. 2021Adversarially Robust Kernel Smoothingcited by 4
  22. 2021Distributionally Robust Optimization with Markovian Datacited by 4
  23. 2022On Certifying and Improving Generalization to Unseen Domainscited by 4
  24. 2023Robustified Learning for Online Optimization with Memory Costscited by 4
  25. 2023Efficient Stochastic Approximation of Minimax Excess Risk Optimizationcited by 4
  26. 2023f-FERM: A Scalable Framework for Robust Fair Empirical Risk Minimizationcited by 4
  27. 2024Towards Generalizing Inferences from Trials to Target Populationscited by 4
  28. 2024Uncertainty Quantification on Graph Learning: A Surveycited by 4
  29. 2021Learning Under Adversarial and Interventional Shiftscited by 3
  30. 2021Robust Graph Learning Under Wasserstein Uncertaintycited by 3
  31. 2021Human Imperceptible Attacks and Applications to Improve Fairnesscited by 3
  32. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  33. 2023Hoeffding's Inequality for Markov Chains under Generalized Concentrability Conditioncited by 3
  34. 2024Rejection via Learning Density Ratioscited by 3
  35. 2024Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Setscited by 3
  36. 2026Distributionally Robust Optimization via Generative Ambiguity Modelingcited by 3
  37. 2021A Note on Optimizing Distributions using Kernel Mean Embeddingscited by 2
  38. 2022Distributionally Robust Domain Adaptationcited by 2

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