Online kernel selection via grouped adversarial bandit model

We study kernel selection for online kernel learning, also known as online kernel selection which can be treated as a sequential decision problem and thus must balance the regret and the time complexity. Existing online kernel selection approaches via expert advice and classical adversarial bandit model can not meet the issue. In this work, we propose a novel grouped adversarial bandit solution to the problem. We first correspond each candidate kernel to a basic arm of an adversarial bandit problem. Then, all of the kernels are divided into several groups where each group is abstracted as a super arm. At each round, we choose a super arm and a basic kernel within the selected super arm, and make prediction by an online kernel learning algorithm. Besides, we introduce a Bernoulli random variable to decide whether to choose all of the rest super arms. Theoretical analysis shows the proposed approach balances the regret and the time complexity explicitly, which could enjoy better pseudo-regret and high probability regret bound than classical adversarial bandit model and lighter time complexity than expert advice model. Experimental results on benchmark datasets verify that the proposed approach balances the efficiency and effectiveness better.