Reviews: Accelerating Stochastic Composition Optimization

First of all, the novelty and originality is a big concern. Not to mention the fact that, the main Theorem 1 assumes no nonsmooth penalty term. So literally, this paper has not really done what they claimed - address nonsmooth regularization penalty without deteriorating the convergence rate. Theorem 2 is more or less just a repetition of Theorem 7 in [Wang et.al, 2016], except with a slightly more general choice of learning rate. Overall, I don't feel the paper has a substantial contribution.