Online learning to rank (LTR) focuses on learning a policy from user interactions that builds a list of items sorted in decreasing order of the item utility. It is a core area in modern interactive systems, such as search engines, recommender systems, or conversational assistants. Previous online LTR approaches either assume the relevance of an item in the list to be independent of other items in the list or the relevance of an item to be a submodular function of the utility of the list. The former type of approach may result in a list of low diversity that has relevant items covering the same aspects, while the latter approaches may lead to a highly diversified list but with some non-relevant items.In this paper, we study an online LTR problem that considers both item relevance and topical diversity. We assume cascading user behavior, where a user browses the displayed list of items from top to bottom and clicks the first attractive item and stops browsing the rest. We propose a hybrid contextual bandit approach, called CascadeHybrid, for solving this problem. CascadeHybrid models item relevance and topical diversity using two independent functions and simultaneously learns those functions from user click feedback. We derive a gap-free bound on the n-step regret of CascadeHybrid. We conduct experiments to evaluate CascadeHybrid on the MovieLens and Yahoo music datasets. Our experimental results show that CascadeHybrid outperforms the baselines on both datasets.

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