mlsanityData to 7 Oct 2026

Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints

arXiv 2210.01413 ↗First posted 4 Oct 2022math.OC cs.LG stat.MLcited by 6

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Abstract (arXiv)

Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary chooses distributions in a suitable optimal transport neighborhood of the empirical measure), provided that suitable martingale constraints are also imposed. Further, we introduce a relaxation of the martingale constraints which not only provides a unified viewpoint to a class of existing robust methods but also leads to new regularization tools. To realize these novel tools, tractable computational algorithms are proposed. As a byproduct, the strong duality theorem proved in this paper can be potentially applied to other problems of independent interest.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 14 of its 34 references that are in the map. First posted on arXiv 4 Oct 2022.

Builds on

14 of 34 references.

References · 14

  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. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  5. 2015Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulationscited by 285
  6. 2016Variance-based regularization with convex objectivescited by 153
  7. 2019Robust Learning with Jacobian Regularizationcited by 127
  8. 2015Distributionally Robust Logistic Regressioncited by 124
  9. 2017Regularization via Mass Transportationcited by 79
  10. 2019Distributionally Robust Optimization and Generalization in Kernel Methodscited by 73
  11. 2019Scaleable input gradient regularization for adversarial robustnesscited by 45
  12. 2018Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemescited by 30
2 more
  1. 2020Generalised Lipschitz Regularisation Equals Distributional Robustnesscited by 14
  2. 2021Distributionally Robust Learning with Stable Adversarial Trainingcited by 14

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 1; 2025: 0; 2026: 2.

6 papers.

  1. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 12
  2. 2024Automatic Outlier Rectification via Optimal Transportcited by 1
  3. 2022Generalized Laplacian Regularized Framelet Graph Neural Networkscited by 0
  4. 2023Robust Regression over Averaged Uncertaintycited by 0
  5. 2026A Distributionally Robust Framework for Learned Reconstructions in Inverse Problemscited by 0
  6. 2026Distributionally robust linear regression through the lens of adversarial trainingcited by 0