Error bounds of adversarial bipartite ranking

Generalization analysis for learning models with adversarial examples has attracted increasing attentions recently. However, the previous theoretical results are usually limited to learning models with the pointwise loss. In this paper, we beyond this restriction by investigating generalization ability of bipartite ranking associated with adversarial perturbations. The upper bounds of adversarial ranking risk are established by formulating the pairwise learning in a minimax framework and introducing the transfer mapping to relate data distributions. In particular, our results are suitable to general loss satisfying Lipschitz conditions, e.g, the logistic loss and the least squared loss.