# NIPS Proceedingsβ

## Contextual Combinatorial Multi-armed Bandits with Volatile Arms and Submodular Reward

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### Abstract

In this paper, we study the stochastic contextual combinatorial multi-armed bandit (CC-MAB) framework that is tailored for volatile arms and submodular reward functions. CC-MAB inherits properties from both contextual bandit and combinatorial bandit: it aims to select a set of arms in each round based on the side information (a.k.a. context) associated with the arms. By volatile arms'', we mean that the available arms to select from in each round may change; and by submodular rewards'', we mean that the total reward achieved by selected arms is not a simple sum of individual rewards but demonstrates a feature of diminishing returns determined by the relations between selected arms (e.g. relevance and redundancy). Volatile arms and submodular rewards are often seen in many real-world applications, e.g. recommender systems and crowdsourcing, in which multi-armed bandit (MAB) based strategies are extensively applied. Although there exist works that investigate these issues separately based on standard MAB, jointly considering all these issues in a single MAB problem requires very different algorithm design and regret analysis. Our algorithm CC-MAB provides an online decision-making policy in a contextual and combinatorial bandit setting and effectively addresses the issues raised by volatile arms and submodular reward functions. The proposed algorithm is proved to achieve $O(cT^{\frac{2\alpha+D}{3\alpha + D}}\log(T))$ regret after a span of $T$ rounds. The performance of CC-MAB is evaluated by experiments conducted on a real-world crowdsourcing dataset, and the result shows that our algorithm outperforms the prior art.