Linear Submodular Bandits and their Application to Diversified Retrieval
Diversified retrieval and online learning are two core research areas in the design of modern information retrieval systems. In this paper, we propose the linear sub-modular bandits problem, which is an online learning setting for optimizing a general class of feature-rich submodular utility models for diversified retrieval. We present an algorithm, called LSBGREEDY, and prove that it efficiently converges to a near-optimal model. As a case study, we applied our approach to the setting of personalized news recommendation, where the system must recommend small sets of news articles selected from tens of thousands of available articles each day. In a live user study, we found that LSBGREEDY significantly outperforms existing online learning approaches.
In this article, we study nonsmooth convex minimax programming problems with cone constraint and abstract constraint. Our aim is to develop sequential Lagrange multiplier rules for this class of problems in the absence of any constraint qualification. These rules are obtained in terms of ∊-subdifferentials of the functions. As an application of these rules, a sequential dual is proposed and sequential duality results are presented.