The reviewers all liked the paper; beside the new model (and its analysis) they particularly liked "anti-concentration" result for UCB. Nevertheless, they pointed out a few issues which should be addressed in the final version. The most important ones are (i) the issue with beta should be properly discussed; (ii) it would be good to have a motivating example which actually matches the model (unlike the current ones); (iii) the algorithm for more than 2 arms seems quite wasteful.