# On a class of adversarial classification problems which admit a continuous solution

arXiv: https://arxiv.org/abs/2502.21170 · HTML: https://mlsanity.com/paper/2502.21170/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2025.

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

- [Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions](https://mlsanity.com/paper/2510.01969/) (2025)

## Abstract (arXiv)

We consider a class of adversarial classification problems in the form of zero-sum games between a classifier and an adversary. The latter is able to corrupt data, at the expense of some optimal transport cost. We show that quite general assumptions on the loss functions of the classifier and the transport cost functions of the adversary ensure the existence of a Nash equilibrium with a continuous (or even Lipschitz) classifier's strategy. We also consider a softmax-like regularization of this problem and present numerical results for this regularization.