# Coresets for Wasserstein Distributionally Robust Optimization Problems

arXiv: https://arxiv.org/abs/2210.04260 · HTML: https://mlsanity.com/paper/2210.04260/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 61 references that are in the map.
- First posted on arXiv 9 Oct 2022.

## Builds on (most cited first, 19 of 19)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Wild Patterns: Ten Years After the Rise of Adversarial Machine Learning](https://mlsanity.com/paper/1712.03141/) (2017)
- [Certifying Some Distributional Robustness with Principled Adversarial Training](https://mlsanity.com/paper/1710.10571/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Stochastic Optimization with Wasserstein Distance](https://mlsanity.com/paper/1604.02199/) (2016)
- [Large-Scale Methods for Distributionally Robust Optimization](https://mlsanity.com/paper/2010.05893/) (2020)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015)
- [Regularization via Mass Transportation](https://mlsanity.com/paper/1710.10016/) (2017)
- [Coresets for Near-Convex Functions](https://mlsanity.com/paper/2006.05482/) (2020)
- [Data-driven Inverse Optimization with Imperfect Information](https://mlsanity.com/paper/1512.05489/) (2015)
- [Wasserstein Distributionally Robust Optimization and Variation Regularization](https://mlsanity.com/paper/1712.06050/) (2017)
- [varepsilon-Coresets for Clustering (with Outliers) in Doubling Metrics](https://mlsanity.com/paper/1804.02530/) (2018)
- [Support Vector Machines under Adversarial Label Contamination](https://mlsanity.com/paper/2206.00352/) (2022)
- [Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine](https://mlsanity.com/paper/2010.12865/) (2020)
- [A Novel Sequential Coreset Method for Gradient Descent Algorithms](https://mlsanity.com/paper/2112.02504/) (2021)
- [Robust and Fully-Dynamic Coreset for Continuous-and-Bounded Learning (With Outliers) Problems](https://mlsanity.com/paper/2107.00068/) (2021)
- [Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls](https://mlsanity.com/paper/1609.07505/) (2016)

## Built on by (most cited first, 6 of 6)

- [Towards Robust Alignment of Language Models: Distributionally Robustifying Direct Preference Optimization](https://mlsanity.com/paper/2407.07880/) (2024)
- [Understanding Contrastive Learning via Distributionally Robust Optimization](https://mlsanity.com/paper/2310.11048/) (2023)
- [Learning from Heterogeneity: Generalizing Dynamic Facial Expression Recognition via Distributionally Robust Optimization](https://mlsanity.com/paper/2507.15765/) (2025)
- [Wasserstein distributional robustness of neural networks](https://mlsanity.com/paper/2306.09844/) (2023)
- [On Robust Wasserstein Barycenter: The Model and Algorithm](https://mlsanity.com/paper/2312.15762/) (2023)
- [Wasserstein distributional adversarial training for deep neural networks](https://mlsanity.com/paper/2502.09352/) (2025)

## Abstract (arXiv)

Wasserstein distributionally robust optimization (textsfWDRO) is a popular model to enhance the robustness of machine learning with ambiguous data. However, the complexity of textsfWDRO can be prohibitive in practice since solving its ``minimax'' formulation requires a great amount of computation. Recently, several fast textsfWDRO training algorithms for some specific machine learning tasks (e.g., logistic regression) have been developed. However, the research on designing efficient algorithms for general large-scale textsfWDROs is still quite limited, to the best of our knowledge. textitCoreset is an important tool for compressing large dataset, and thus it has been widely applied to reduce the computational complexities for many optimization problems. In this paper, we introduce a unified framework to construct the ε-coreset for the general textsfWDRO problems. Though it is challenging to obtain a conventional coreset for textsfWDRO due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of textsfWDRO. Also, the error introduced by the dual coreset can be theoretically guaranteed for the original textsfWDRO objective. To construct the dual coreset, we propose a novel grid sampling approach that is particularly suitable for the dual formulation of textsfWDRO. Finally, we implement our coreset approach and illustrate its effectiveness for several textsfWDRO problems in the experiments.