939314105ce8701e67489642ef4d49e8-AuthorFeedback.pdf

We answer your main questions as follows. "Is there any hope to avoid the We will add a remark in the paper to discuss this point more thoroughly. Question 2. "Technically, I think in order for Lemma 4 to hold, f needs to be defined on the whole vector space" The issue has also been identified by Reviewer #3. We will improve the paper writing to make this point more clear. Question 2. "what regret ... if ... only access to 1 gradient query per step, rather than the two used in OEGD." We address your main questions as follows. Question 1. "how would the lower-bound of function appear in your bounds if we assume they are not positive" Question 2. "how would the algorithms / results change if 0 is not in X?" Answer 2. There are three places we use this assumption: About the self-bounding property of smooth functions, you are absolutely correct. For other minor issues, we will carefully revise the paper according to your constructive comments. Below we address your concerns and clarify the misunderstandings. Question 2. "The novelty of the paper is limited.