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

TL;DR

This paper studies adversarial classification as a zero-sum game where the adversary corrupts data with a cost, proving the existence of continuous equilibrium strategies under general conditions and exploring regularized versions with numerical results.

Contribution

It establishes the existence of continuous Nash equilibria in adversarial classification games with general loss and transport costs, and analyzes a regularized variant.

Findings

Existence of continuous (Lipschitz) Nash equilibria under broad assumptions

Regularized problem admits a softmax-like solution

Numerical experiments demonstrate the regularization approach

Abstract

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.