In contrast to offline kernel selection, online kernel selection must rise to the new challenges of passing the training set once, selecting optimal kernels and updating hypotheses at each round, enjoying a sublinear regret bound for online kernel learning, and requiring a constant maintenance time complexity at each round and an efficient overall time complexity integrated with online kernel learning. However, most of existing online kernel selection approaches can not meet the new challenges. To address this issue, we propose a novel online kernel selection approach via the incremental sketched kernel alignment criterion, which meets all the new challenges. We first define the incremental sketched kernel alignment (ISKA) criterion, which estimates the kernel alignment and can be computed incrementally and efficiently. When applying the proposed ISKA criterion to online kernel selection, we adopt the subclass coherence to maintain the hypothesis space, select the optimal kernel at each round using the median of the ISKA criterion estimates, and update the hypothesis following the online gradient decent method. We prove that the ISKA criterion is an unbiased estimate of the maximum mean discrepancy, enjoys the optimal logarithmic regret bound for online kernel learning, and has a constant maintenance time complexity at each round and a logarithmic overall time complexity integrated with online kernel learning. Empirical studies demonstrate that the proposed online kernel selection approach is computationally efficient while maintaining comparable accuracy for online kernel learning.
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