Adversarial Classification via Distributional Robustness with Wasserstein Ambiguity

TL;DR

This paper introduces a distributionally robust adversarial classification model using Wasserstein ambiguity, linking it to CVaR and maximum-margin classifiers, and demonstrates effective optimization despite nonconvexity.

Contribution

It reformulates the robust classification problem as a regularized ramp loss minimization and analyzes convergence properties of standard optimization methods.

Findings

The model minimizes CVaR of misclassification distance under Wasserstein ambiguity.

Standard descent methods often find the global minimum despite nonconvexity.

For certain distributions, the only stationary point is the global minimizer.

Abstract

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.