text: Summary ******* The paper provides a collection of existing results in statistics. Comments ******** Page 1: references to Q-learning and Policy-gradients look awkwardly recent,  given that these have been around for several decades. I dont get what is the novelty in this paper.  There is no doubt that all the tools that are detailed here are extremely useful and powerful results in mathematical statistics.  But they are all known. The Gibbs variational principle is folklore,  Proposition 1,2 are available in all good text books on the topic,  and Proposition 4 is nothing but a transportation Lemma. Now, Proposition 3 is about soft-Bellman operators.  This perhaps is less standard  because contraction property of soft-Bellman operator in infinite norm is more recent than for Bellman operators. But as mentioned by the authors, this is not new either.  Also I don't really see the point of providing the proofs of these results in the main material, and not for instance in appendix,  as there is no novelty either in the proof techniques. I don't get the sentence "we have restricted so far the proof in the bandit setting":  bandits are not even mentioned earlier. Decision ******** I am sorry but unless I missed something (that then should be clarified) this seems to be an empty paper: Strong reject.