Generalization analysis of adversarial pairwise learning

Adversarial pairwise learning has become the predominant method to enhance the discrimination ability of models against adversarial attacks, achieving tremendous success in various application fields. Despite excellent empirical performance, adversarial robustness and generalization of adversarial pairwise learning remain poorly understood from the theoretical perspective. This paper moves towards this by establishing the high- probability generalization bounds. Our bounds generally apply to various models and pairwise learning tasks. We give application examples involving explicit bounds of adversarial bipartite ranking and adversarial metric learning to illustrate how the theoretical results can be extended. Furthermore, we develop the optimistic generalization bound at order c(n-1) on the sample size n by leveraging local Rademacher complexity. Our analysis provides meaningful theoretical guidance for improving adversarial robustness through feature size and regularization. Experimental results validate theoretical findings.