# Fast Epigraphical Projection-based Incremental Algorithms for Wasserstein Distributionally Robust Support Vector Machine

arXiv: https://arxiv.org/abs/2010.12865 · HTML: https://mlsanity.com/paper/2010.12865/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2020.

## Built on by (most cited first, 10 of 10)

- [Fast Distributionally Robust Learning with Variance Reduced Min-Max Optimization](https://mlsanity.com/paper/2104.13326/) (2021)
- [Unifying Distributionally Robust Optimization via Optimal Transport Theory](https://mlsanity.com/paper/2308.05414/) (2023)
- [Last Iterate Convergence of Incremental Methods and Applications in Continual Learning](https://mlsanity.com/paper/2403.06873/) (2024)
- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Coresets for Wasserstein Distributionally Robust Optimization Problems](https://mlsanity.com/paper/2210.04260/) (2022)
- [Universal generalization guarantees for Wasserstein distributionally robust models](https://mlsanity.com/paper/2402.11981/) (2024)
- [Distributionally Robust Graph Learning from Smooth Signals under Moment Uncertainty](https://mlsanity.com/paper/2105.05458/) (2021)
- [Distributionally Time-Varying Online Stochastic Optimization under Polyak-Lojasiewicz Condition with Application in Conditional Value-at-Risk Statistical Learning](https://mlsanity.com/paper/2309.09411/) (2023)
- [An Inexact Halpern Iteration with Application to Distributionally Robust Optimization](https://mlsanity.com/paper/2402.06033/) (2024)
- [Distributionally Robust Optimization with Adversarial Data Contamination](https://mlsanity.com/paper/2507.10718/) (2025)

## Abstract (arXiv)

Wasserstein Distributionally Robust Optimization (DRO) is concerned with finding decisions that perform well on data that are drawn from the worst-case probability distribution within a Wasserstein ball centered at a certain nominal distribution. In recent years, it has been shown that various DRO formulations of learning models admit tractable convex reformulations. However, most existing works propose to solve these convex reformulations by general-purpose solvers, which are not well-suited for tackling large-scale problems. In this paper, we focus on a family of Wasserstein distributionally robust support vector machine (DRSVM) problems and propose two novel epigraphical projection-based incremental algorithms to solve them. The updates in each iteration of these algorithms can be computed in a highly efficient manner. Moreover, we show that the DRSVM problems considered in this paper satisfy a H"olderian growth condition with explicitly determined growth exponents. Consequently, we are able to establish the convergence rates of the proposed incremental algorithms. Our numerical results indicate that the proposed methods are orders of magnitude faster than the state-of-the-art, and the performance gap grows considerably as the problem size increases.