[Clarity] * What is the value of the c constant (MaxGapUCB algorithm) used in experiments? How was it determined? How does it impact the performance of MaxGapUCB? * The experiment results could be discussed more. For example, should we conclude from the Streetview experiment that MaxGapTop2UCB is better than the other ones? [Significance] * The real-world applications of this new problem setting are not clear. The authors mention applicability to sorting/ranking. It seems like this would require a recursive application of proposed algorithms to recover partial ordering. However, the procedure to find the upper bounds on gaps (Alg. 4) has complexity K^2, where K is the number of arms. How would that translate in computational complexity when solving a ranking problem? Minor details: * T_a(t) is used in Section 3.1, but only defined in Section 4. * The placement of Figure 2 is confusing. --------------------------------------------------------------------------- I have read the rebuttal. Though the theoretical contribution seems rather low given existing work on pure exploration, the authors have convinced me of the potential impacts of this work.
* T_a(t) is used in Section 3.1, but only defined in Section 4.