# Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes

arXiv: https://arxiv.org/abs/1810.02403 · HTML: https://mlsanity.com/paper/1810.02403/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2018.

## Built on by (most cited first, 30 of 30)

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- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
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- [Smooth p-Wasserstein Distance: Structure, Empirical Approximation, and Statistical Applications](https://mlsanity.com/paper/2101.04039/) (2021)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Robustifying Conditional Portfolio Decisions via Optimal Transport](https://mlsanity.com/paper/2103.16451/) (2021)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Robust Estimation under the Wasserstein Distance](https://mlsanity.com/paper/2302.01237/) (2023)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Distributionally Robust Optimization via Iterative Algorithms in Continuous Probability Spaces](https://mlsanity.com/paper/2412.20556/) (2024)
- [Worst-case generation via minimax optimization in Wasserstein space](https://mlsanity.com/paper/2512.08176/) (2025)
- [Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints](https://mlsanity.com/paper/2210.01413/) (2022)
- [Adversarially Robust Kernel Smoothing](https://mlsanity.com/paper/2102.08474/) (2021)
- [Robust Graph Learning Under Wasserstein Uncertainty](https://mlsanity.com/paper/2105.04210/) (2021)
- [Human Imperceptible Attacks and Applications to Improve Fairness](https://mlsanity.com/paper/2111.15603/) (2021)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [LLM Embeddings Improve Test-time Adaptation to Tabular Y|X-Shifts](https://mlsanity.com/paper/2410.07395/) (2024)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (2024)
- [Wasserstein Distributionally Robust Regret Optimization](https://mlsanity.com/paper/2504.10796/) (2025)
- [Distributionally robust risk evaluation with a causality constraint and structural information](https://mlsanity.com/paper/2203.10571/) (2022)
- [Adjusted Wasserstein Distributionally Robust Estimator in Statistical Learning](https://mlsanity.com/paper/2303.15579/) (2023)
- [A stochastic smoothing framework for nonconvex-nonconcave minEmax problems with applications to Wasserstein distributionally robust optimization](https://mlsanity.com/paper/2502.17602/) (2025)
- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)
- [Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2512.12550/) (2025)
- [Nonlinear Distributionally Robust Optimization](https://mlsanity.com/paper/2306.03202/) (2023)
- [Distributionally Robust Federated Learning: An ADMM Algorithm](https://mlsanity.com/paper/2503.18436/) (2025)
- [New Algorithmic Directions in Optimal Transport and Applications for Product Spaces](https://mlsanity.com/paper/2509.21502/) (2025)
- [Natural Geometry of Robust Data Attribution: From Convex Models to Deep Networks](https://mlsanity.com/paper/2512.09103/) (2025)

## Abstract (arXiv)

We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded in the DRO problem (e.g. strong convexity even if the non-DRO problem was not strongly convex, a suitable scaling of the Lagrangian for the DRO constraint, etc. which are crucial for the design of efficient algorithms). As a consequence of these results, one can develop efficient optimization procedures which have the same sample and iteration complexity as a natural non-DRO benchmark algorithm such as stochastic gradient descent.