Generalization Bounds for Ranking Algorithms via Algorithmic Stability

The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained much attention in machine learning. We study generalization properties of ranking algorithms using the notion of algorithmic stability; in particular, we derive generalization bounds for ranking algorithms that have good stability properties. We show that kernel-based ranking algorithms that perform regularization in a reproducing kernel Hilbert space have such stability properties, and therefore our bounds can be applied to these algorithms; this is in contrast with generalization bounds based on uniform convergence, which in many cases cannot be applied to these algorithms. Our results generalize earlier results that were derived in the special setting of bipartite ranking (Agarwal and Niyogi, 2005) to a more general setting of the ranking problem that arises frequently in applications.