# Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2512.12550 · HTML: https://mlsanity.com/paper/2512.12550/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 80 references that are in the map.
- First posted on arXiv 14 Dec 2025.

## Builds on (most cited first, 30 of 49)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Theoretical guarantees for approximate sampling from smooth and log-concave densities](https://mlsanity.com/paper/1412.7392/) (2014)
- [Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm](https://mlsanity.com/paper/1507.05021/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Convergence of Langevin MCMC in KL-divergence](https://mlsanity.com/paper/1705.09048/) (2017)
- [The Principles of Diffusion Models](https://mlsanity.com/paper/2510.21890/) (2025)
- [Stochastic Particle Gradient Descent for Infinite Ensembles](https://mlsanity.com/paper/1712.05438/) (2017)
- [Biased Stochastic First-Order Methods for Conditional Stochastic Optimization and Applications in Meta Learning](https://mlsanity.com/paper/2002.10790/) (2020)
- [Stochastic Frank-Wolfe Methods for Nonconvex Optimization](https://mlsanity.com/paper/1607.08254/) (2016)
- [Sinkhorn Distributionally Robust Optimization](https://mlsanity.com/paper/2109.11926/) (2021)
- [Randomized Stochastic Variance-Reduced Methods for Multi-Task Stochastic Bilevel Optimization](https://mlsanity.com/paper/2105.02266/) (2021)
- [Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes](https://mlsanity.com/paper/1810.02403/) (2018)
- [Implicit Diffusion: Efficient Optimization through Stochastic Sampling](https://mlsanity.com/paper/2402.05468/) (2024)
- [Provable Bayesian Inference via Particle Mirror Descent](https://mlsanity.com/paper/1506.03101/) (2015)
- [Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence](https://mlsanity.com/paper/2202.12183/) (2022)
- [Sample Complexity of Sample Average Approximation for Conditional Stochastic Optimization](https://mlsanity.com/paper/1905.11957/) (2019)
- [A Unified Theory of Robust and Distributionally Robust Optimization via the Primal-Worst-Equals-Dual-Best Principle](https://mlsanity.com/paper/2105.00760/) (2021)
- [Improved Particle Approximation Error for Mean Field Neural Networks](https://mlsanity.com/paper/2405.15767/) (2024)
- [Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization](https://mlsanity.com/paper/2206.00260/) (2022)
- [Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems](https://mlsanity.com/paper/2312.01127/) (2023)
- [Annealing Flow Generative Models Towards Sampling High-Dimensional and Multi-Modal Distributions](https://mlsanity.com/paper/2409.20547/) (2024)
- [Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Bandits](https://mlsanity.com/paper/2309.08748/) (2023)

## Built on by (most cited first, 1 of 1)

- [Generative Neural Networks for Sinkhorn Distributionally Robust Hypothesis Testing](https://mlsanity.com/paper/2608.22746/) (2026)

## Abstract (arXiv)

Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized Wasserstein distance, referred to as Sinkhorn DRO. Existing work primarily addresses Sinkhorn DRO from a dual perspective, leveraging its formulation as a conditional stochastic optimization problem, for which many stochastic gradient methods are applicable. However, the theoretical analyses of such methods often rely on the boundedness of the loss function, and it is indirect to obtain the worst-case distribution associated with Sinkhorn DRO. In contrast, we study Sinkhorn DRO from the primal perspective, by reformulating it as a bilevel program with several infinite-dimensional lower-level subproblems over probability space. This formulation enables us to simultaneously obtain the optimal robust decision and the worst-case distribution, which is valuable in practical settings, such as generating stress-test scenarios or designing robust learning algorithms. We propose both double-loop and single-loop sampling-based algorithms with theoretical guarantees to solve this bilevel program. Finally, we demonstrate the effectiveness of our approach through a numerical study on adversarial classification.