Comparator-Adaptive Convex Bandits

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

AuthorFeedback »Bibtex »MetaReview »Paper »Review »Supplemental »


Dirk van der Hoeven, Ashok Cutkosky, Haipeng Luo


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.