Reviewer

We would like to thank the reviewers for their helpful comments. We will revise accordingly in the revision. We will revise Lemma C.2 for handling general RKHS in the revision. Moreover the NTK induced by sinusoidal activations recovers the Gaussian RBF (See {2}). For polynomial decay we can also obtain a sublinear regret, which gives a poly ( H, 1/ε) computation complexity.