Uniform Convergence, Stability and Learnability for Ranking Problems / 1337
Wei Gao, Zhi-Hua Zhou

Most studies were devoted to the design of efficient algorithms and the evaluation and application on diverse ranking problems, whereas few work has been paid to the theoretical studies on ranking learnability. In this paper, we study the relation between uniform convergence, stability and learnability of ranking. In contrast to supervised learning where the learnability is equivalent to uniform convergence, we show that the ranking uniform convergence is sufficient but not necessary for ranking learnability with AERM, and we further present a sufficient condition for ranking uniform convergence with respect to bipartite ranking loss. Considering the ranking uniform convergence being unnecessary for ranking learnability, we prove that the ranking average stability is a necessary and sufficient condition for ranking learnability.