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Sinkhorn Distributionally Robust Optimization

arXiv 2109.11926 ↗First posted 24 Sep 2021math.OC cs.LG stat.MLcited by 38

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Abstract (arXiv)

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport costs, and loss functions. To solve the dual reformulation, we develop a stochastic mirror descent algorithm with biased subgradient estimators and derive its computational complexity guarantees. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 67 of its 161 references that are in the map. First posted on arXiv 24 Sep 2021.

Builds on

67 of 161 references.

References · 67

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Explaining and Harnessing Adversarial Examplescited by 7,287
  3. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  4. 2021Convex optimizationcited by 2,479
  5. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,277
  6. 2016Practical Black-Box Attacks against Machine Learningcited by 893
  7. 2017Ensemble Adversarial Training: Attacks and Defensescited by 833
  8. 2015The Limitations of Deep Learning in Adversarial Settingscited by 784
  9. 2018Computational Optimal Transportcited by 765
  10. 2015Distillation as a Defense to Adversarial Perturbations against Deep Neural Networkscited by 675
  11. 2015Optimal Transport for Domain Adaptationcited by 457
  12. 2017Learning Generative Models with Sinkhorn Divergencescited by 310
38 more
  1. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 285
  2. 2017Joint Distribution Optimal Transportation for Domain Adaptationcited by 280
  3. 2017Near-linear time approximation algorithms for optimal transport via Sinkhorn iterationcited by 219
  4. 2016Stochastic Optimization for Large-scale Optimal Transportcited by 188
  5. 2016Distributionally Robust Stochastic Optimization with Wasserstein Distancecited by 182
  6. 2016Statistics of Robust Optimization: A Generalized Empirical Likelihood Approachcited by 182
  7. 2020Large-Scale Methods for Distributionally Robust Optimizationcited by 179
  8. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  9. 2020Adversarial Robustness: From Self-Supervised Pre-Training to Fine-Tuningcited by 152
  10. 2013Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimizationcited by 142
  11. 2014From Predictive to Prescriptive Analyticscited by 142
  12. 2017Non-convex Optimization for Machine Learningcited by 132
  13. 2015Distributionally Robust Logistic Regressioncited by 124
  14. 2014Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functionscited by 93
  15. 2017Regularization via Mass Transportationcited by 79
  16. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  17. 2017On the regularization of Wasserstein GANscited by 65
  18. 2018Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distancecited by 56
  19. 2018A Single Time-Scale Stochastic Approximation Method for Nested Stochastic Optimizationcited by 53
  20. 2019Wasserstein Robust Reinforcement Learningcited by 50
  21. 2020Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionalitycited by 49
  22. 2020Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learningcited by 46
  23. 2020Projection Robust Wasserstein Distance and Riemannian Optimizationcited by 45
  24. 2020A Distributionally Robust Approach to Fair Classificationcited by 43
  25. 2019Distributionally Robust Reinforcement Learningcited by 40
  26. 2020Distributional Robustness and Regularization in Reinforcement Learningcited by 39
  27. 2016Geometric Median in Nearly Linear Timecited by 38
  28. 2019On the Efficiency of Entropic Regularized Algorithms for Optimal Transportcited by 34
  29. 2018Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemescited by 30
  30. 2018Wasserstein Distributionally Robust Stochastic Control: A Data-Driven Approachcited by 27
  31. 2020A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distancecited by 27
  32. 2021Statistical Analysis of Wasserstein Distributionally Robust Estimatorscited by 27
  33. 2018Multi-Level Stochastic Gradient Methods for Nested Composition Optimizationcited by 24
  34. 2018Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distancescited by 24
  35. 2019Confidence Regions in Wasserstein Distributionally Robust Estimationcited by 24
  36. 2018Natural gradient via optimal transportcited by 19
  37. 2019Sample Complexity of Sample Average Approximation for Conditional Stochastic Optimizationcited by 19
  38. 2021Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimizationcited by 19

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 10; 2024: 8; 2025: 9; 2026: 9.

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  1. 2023A Guide Through the Zoo of Biased SGDcited by 39
  2. 2022Holistic Robust Data-Driven Decisionscited by 17
  3. 2022Stochastic Constrained DRO with a Complexity Independent of Sample Sizecited by 16
  4. 2023Contextual Stochastic Bilevel Optimizationcited by 14
  5. 2023Flow-based Distributionally Robust Optimizationcited by 13
  6. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 12
  7. 2023Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Modelscited by 9
  8. 2023Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Banditscited by 9
  9. 2023Provably Convergent Policy Optimization via Metric-aware Trust Region Methodscited by 6
  10. 2024Toward Robust Neural Reconstruction from Sparse Point Setscited by 5
  11. 2025DRO: A Python Library for Distributionally Robust Optimization in Machine Learningcited by 5
  12. 2023Stochastic Approximation Approaches to Group Distributionally Robust Optimization and Beyondcited by 4
26 more
  1. 2024Non-Convex Robust Hypothesis Testing using Sinkhorn Uncertainty Setscited by 4
  2. 2024Statistical and Computational Guarantees of Kernel Max-Sliced Wasserstein Distancescited by 4
  3. 2024Multi-level Monte-Carlo Gradient Methods for Stochastic Optimization with Biased Oraclescited by 4
  4. 2024textttskwdro: a library for Wasserstein distributionally robust machine learningcited by 4
  5. 2025Improved Stochastic Optimization of LogSumExpcited by 4
  6. 2024Large-Scale Non-convex Stochastic Constrained Distributionally Robust Optimizationcited by 3
  7. 2025Nested Stochastic Algorithm for Generalized Sinkhorn distance-Regularized Distributionally Robust Optimizationcited by 3
  8. 2026Distributionally Robust Optimization via Generative Ambiguity Modelingcited by 3
  9. 2023Optimal Transport Regularized Divergences: Application to Adversarial Robustnesscited by 2
  10. 2024Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimatorscited by 2
  11. 2024Regularization for Adversarial Robust Learningcited by 2
  12. 2025Leveraging Machine Unlearning for Cost-Efficient Preference Alignmentcited by 2
  13. 2025Gradient Flow Sampler-based Distributionally Robust Optimizationcited by 2
  14. 2025A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimizationcited by 1
  15. 2025Distributionally Robust Deep Q-Learningcited by 1
  16. 2025Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimizationcited by 1
  17. 2023Nonlinear Distributionally Robust Optimizationcited by 0
  18. 2025Duality and Policy Evaluation in Distributionally Robust Bayesian Diffusion Controlcited by 0
  19. 2026Multivariate Time Series Data Imputation via Distributionally Robust Regularizationcited by 0
  20. 2026Statistical Guarantees for Distributionally Robust Optimization with Optimal Transport and OT-Regularized Divergencescited by 0
  21. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
  22. 2026Generative Distributionally Robust Optimizationcited by 0
  23. 2026Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testingcited by 0
  24. 2026Brenier Meets Adversarial Training: Optimal Transport Geometry for Robust Learningcited by 0
  25. 2026Beyond Empirical Support: Structured Outlier Generation via Sinkhorn Optimal Transportcited by 0
  26. 2026Distributionally Robust Schr"odinger Bridgecited by 0