Adversarial Surrogate Risk Bounds for Binary Classification

TL;DR

This paper develops bounds on the rate at which adversarial surrogate risk minimization converges to optimal adversarial classification risk in binary classification, enhancing understanding of adversarial training effectiveness.

Contribution

It introduces surrogate risk bounds that quantify the convergence rate of adversarial classification risk, addressing a gap in existing theoretical analyses.

Findings

Provides the first bounds on convergence rates for adversarial surrogate risk minimization.

Quantifies how quickly adversarial classification risk approaches its optimum.

Enhances theoretical understanding of adversarial training in binary classification.

Abstract

A central concern in classification is the vulnerability of machine learning models to adversarial attacks. Adversarial training is one of the most popular techniques for training robust classifiers, which involves minimizing an adversarial surrogate risk. Recent work has characterized the conditions under which any sequence minimizing the adversarial surrogate risk also minimizes the adversarial classification risk in the binary setting, a property known as adversarial consistency. However, these results do not address the rate at which the adversarial classification risk approaches its optimal value along such a sequence. This paper provides surrogate risk bounds that quantify that convergence rate.