Comparator-Adaptive Convex Bandits

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Authors

Dirk van der Hoeven, Ashok Cutkosky, Haipeng Luo

Abstract

<p>We study bandit convex optimization methods that adapt to the norm of the comparator, a topic that has only been studied before for its full-information counterpart. Specifically, we develop convex bandit algorithms with regret bounds that are small whenever the norm of the comparator is small. We first use techniques from the full-information setting to develop comparator-adaptive algorithms for linear bandits. Then, we extend the ideas to convex bandits with Lipschitz or smooth loss functions, using a new single-point gradient estimator and carefully designed surrogate losses.</p>