1. There have been several results on the problems of batched top-k ranking and fully adaptive coarse ranking in recent years. From that point of view the results in this paper are not particularly surprising. Even the idea that one can reduce the size of active arm set by a factor of n^{1/R} has appeared in [37] for the problem of collaborative top-1 ranking. However, the main novelty in this paper seems to be the application of this idea for the problem of coarse ranking using a successive-accepts-and-rejects type algorithm. 2. Also, proving lower bounds for round complexity is the major chuck of work involved in proving results for batched ranking problems. However, this paper exploits an easy reduction from the problem of collaborative ranking, and hence, the lower bound results follow as an easy corollary of these collaborative ranking results.
2. Also, proving lower bounds for round complexity is the major chuck of work involved in proving results for batched ranking problems. However, this paper exploits an easy reduction from the problem of collaborative ranking, and hence, the lower bound results follow as an easy corollary of these collaborative ranking results.