Generalization analysis of listwise learning-to-rank algorithms

This paper presents theoretical analysis on the generalization ability of listwise learning-to-rank algorithms using Rademacher Average. The paper first proposes a theoretical framework for ranking and then proves a theorem which gives a gen-eralization bound to a listwise ranking algorithm based on Rademacher Average of the class of compound functions operating on the corresponding listwise loss function and the ranking model. It then derives Rademecher Average of the com-pound function classes for the existing listwise ranking algorithms of ListMLE, ListNet and RankCosine. It also discusses the tightness of generalization bounds in different situations, such as the bounds w.r.t. different list lengths, different transformation functions, and so on. To the best of our knowledge, this is the first paper that formally addresses the theoretical framework and the generalization ability of listwise ranking algorithms. The theoretical findings are useful for the design and parameter tuning of listwise ranking algorithms.