Comparator-adaptive Convex Bandits

• URL: http://arxiv.org/abs/2007.08448v1
• Date: Thu, 16 Jul 2020 16:33:35 GMT
• Title: Comparator-adaptive Convex Bandits
• Authors: Dirk van der Hoeven and Ashok Cutkosky and Haipeng Luo
• Abstract summary: We develop convex bandit algorithms with regret bounds that are small whenever the norm of the comparator is small. We extend the ideas to convex bandits with Lipschitz or smooth loss functions.
• Score: 77.43350984086119
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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