Adversarial Surrogate Risk Bounds for Binary Classification
This work addresses a theoretical gap in adversarial robustness for binary classification, offering incremental insights into convergence rates.
The paper tackles the problem of quantifying the convergence rate of adversarial classification risk to its optimal value for binary classifiers trained by minimizing adversarial surrogate risk, providing surrogate risk bounds that address this gap.
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.