We first redefine notation for clarity and then provide the proofs of the results in the main paper. Now we first prove that the iteration in Eq.2 has a fixed point. Proof of Lemma 3.1: Let We present the bound on using empirical Bellman operator compared to the true Bellman operator. The proof can be found in [6]. Proof of Theorem 3.4: Recall that the expression of the V -function iterate is given by: Proof of Theorem 3.6: The proof of this statement is divided into two parts.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

You guess is as good as mine as to why a film about blockchain technology needs to be filmed this way, but Doug Liman has been connected with plenty of unusual projects in the past, including a rumored Tom Cruise film that was supposed to film on the International Space Station.

Neural Information Processing Systems http://nips.cc/

We thank the reviewers for the detailed and insightful reviews. As the reviews noted, our work 1) introduces "novel Smith et al. [2017] make an explicit connection between small vs. large batch "A small discussion on if the phenomenon has been observed for different datasets/tasks with different optimizers" The phenomenon may not be true for other optimizers such as Adam, though. "concept of "memorizable and generalizable", though intuitive, is sketchy and not formally explained ... authors We acknowledge that the terms "memorizable" and "generalizable" are potentially confusing. We will revise our terminology to clarify this distinction. By "inherently noisy", we refer to the fact that high noise in the datapoints will necessitate larger sample complexity.