Additional Feedback: The authors propose the SDA approach, which has the potential to be an alternative to UCB and Thompson sampling for bandit learning. The main advantage of the proposed approach is that it is non-parametric, and for exponential families of distritions, it could achieve the optimal regret bound matching the lower bound, without knowing which distribution family the unknown distribution belongs to. However, I feel that achieve optimal regret guarantee is mostly theoretical interest. UCB may not be optimal in this sense but it could achieve consistent regret gurantee for all distributions. RB-SDA algorithm, it is unclear to me if its theoretical guarantee of O(log T) regret bound could be achieved for any distribution.

The panel of knowledgeable reviewers is clearly in favor of this paper and its results. The author response also helped significantly to address most concerns raised by the initial reviews. Hence, I am glad to recommend acceptance.

In this paper we propose the first multi-armed bandit algorithm based on re-sampling that achieves asymptotically optimal regret simultaneously for different families of arms (namely Bernoulli, Gaussian and Poisson distributions). Unlike Thompson Sampling which requires to specify a different prior to be optimal in each case, our proposal RB-SDA does not need any distribution-dependent tuning. RB-SDA belongs to the family of Sub-sampling Duelling Algorithms (SDA) which combines the sub-sampling idea first used by the BESA and SSMC algorithms with different sub-sampling schemes. In particular, RB-SDA uses Random Block sampling. We perform an experimental study assessing the flexibility and robustness of this promising novel approach for exploration in bandit models.