We thank the reviewers for their constructive comments

We thank the reviewers for their constructive comments. The two terms on the RHS of Eq. (13) are monotone increasing functions, and Using our Lemma 5.1's proof, Lemma 5.8 and Theorem 2's proof in Srinivas et al [19], the regret bound GP-UCB is chosen as it has ability to analyze convergence, which is very important in the unknown search space setting. EI convergence can be shown only in noiseless setting, PI/ES/PES do not have convergence proof yet). Thank you for the compliment though. We have conducted more experiments with the 10-dimensional functions Ackley10 and Levy10.