# Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity

arXiv: https://arxiv.org/abs/2005.13815 · HTML: https://mlsanity.com/paper/2005.13815/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2020.

## Built on by (most cited first, 8 of 8)

- [Wasserstein Robust Classification with Fairness Constraints](https://mlsanity.com/paper/2103.06828/) (2021)
- [Coordinate Linear Variance Reduction for Generalized Linear Programming](https://mlsanity.com/paper/2111.01842/) (2021)
- [A first-order augmented Lagrangian method for constrained minimax optimization](https://mlsanity.com/paper/2301.02060/) (2023)
- [Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimization](https://mlsanity.com/paper/2303.03900/) (2023)
- [Improving Mixup Calibration with Wasserstein Distributionally Robust Optimization](https://mlsanity.com/paper/2506.17874/) (2025)
- [A Unified Optimization Framework for Multiclass Classification with Structured Hyperplane Arrangements](https://mlsanity.com/paper/2510.05047/) (2025)
- [A first-order method for nonconvex-strongly-concave constrained minimax optimization](https://mlsanity.com/paper/2512.22909/) (2025)
- [Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classification](https://mlsanity.com/paper/2609.23688/) (2026)

## Abstract (arXiv)

We study a model for adversarial classification based on distributionally robust chance constraints. We show that under Wasserstein ambiguity, the model aims to minimize the conditional value-at-risk of the distance to misclassification, and we explore links to adversarial classification models proposed earlier and to maximum-margin classifiers. We also provide a reformulation of the distributionally robust model for linear classification, and show it is equivalent to minimizing a regularized ramp loss objective. Numerical experiments show that, despite the nonconvexity of this formulation, standard descent methods appear to converge to the global minimizer for this problem. Inspired by this observation, we show that, for a certain class of distributions, the only stationary point of the regularized ramp loss minimization problem is the global minimizer.