mlsanityData to 14 Oct 2026

Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization

arXiv 2303.03900 ↗First posted 7 Mar 2023math.OC cs.AI stat.MLcited by 8

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Abstract (arXiv)

We study optimal transport-based distributionally robust optimization problems where a fictitious adversary, often envisioned as nature, can choose the distribution of the uncertain problem parameters by reshaping a prescribed reference distribution at a finite transportation cost. In this framework, we show that robustification is intimately related to various forms of variation and Lipschitz regularization even if the transportation cost function fails to be (some power of) a metric. We also derive conditions for the existence and the computability of a Nash equilibrium between the decision-maker and nature, and we demonstrate numerically that nature's Nash strategy can be viewed as a distribution that is supported on remarkably deceptive adversarial samples. Finally, we identify practically relevant classes of optimal transport-based distributionally robust optimization problems that can be addressed with efficient gradient descent algorithms even if the loss function or the transportation cost function are nonconvex (but not both at the same time).

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 54 of its 112 references that are in the map. First posted on arXiv 7 Mar 2023.

Builds on

54 of 112 references.

References · 54

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38 more
  1. 2016Statistics of Robust Optimization: A Generalized Empirical Likelihood Approachcited by 183
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 1; 2026: 4.

8 papers.

  1. 2023Outlier-Robust Wasserstein DROcited by 16
  2. 2023Unifying Distributionally Robust Optimization via Optimal Transport Theorycited by 13
  3. 2023Nonlinear Distributionally Robust Optimizationcited by 0
  4. 2025Provable Robust Overfitting Mitigation in Wasserstein Distributionally Robust Optimizationcited by 0
  5. 2026Risk-Averse Wasserstein Distributionally Robust Online Learningcited by 0
  6. 2026Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testingcited by 0
  7. 2026The Value of Human Expertisecited by 0
  8. 2026Distributionally robust linear regression through the lens of adversarial trainingcited by 0