Generalization bounds of adversarial bipartite ranking with pairwise perturbation

Investigating the generalization and robustness of adversarial learning is an active research topic due to its implications in designing robust models for a wide range of machine learning tasks. In this paper, we aim to investigate the adversarially robust generalization of bipartite ranking against pairwise perturbation attacks from the lens of learning theory. We establish high-probability generalization error bounds of linear hypotheses and multi-layer neural networks for bipartite ranking under adversarial attacks, by developing Rademacher complexity over i.i.d. sample blocks and covering numbers. Our results provide a theoretical characterization of the interplay between generalization error and perturbation-related factors, revealing the important impact of feature dimension and weight regularization for achieving good generalization performance. Experimental results on real-world datasets validate the effectiveness of our theoretical findings.