Novel Non-convex Online Algorithms for Robust Ranking

Abstract

Recently increasing attention has been focused on learning to rank, which aims to learn a ranking function from a set of training data with relevance labels. Many of the ranking algorithms are based on the pairwise preference framework. However, one disadvantage of pairwise ranking is that it is sensitive to the outliers. To tackle the problem, in this paper, we propose two novel online algorithms based on non-convex Ramp Loss which can suppress the influence of outliers. The first one directly defines a new objective function based on Ramp Loss. Considering that the objective function is nonconvex, we use the Concave-convex Procedure (CCCP) for convex approximation, then design an online algorithm based on Dual Coordinate Descend Method to learn the final ranking model. The second algorithm applies selective sampling technology in the training phase. It ignores the instances that lie in the flat region of the Ramp Loss in advance, before they are processed by the learner. Experimental results show that the algorithms we proposed have significant robustness to outliers and yield better generalization performance than the baseline rankers, and the results also prove that our algorithms have less computational running time for their less support vectors.