Reviews: NESTT: A Nonconvex Primal-Dual Splitting Method for Distributed and Stochastic Optimization

The idea of addressing finite-sum problems through augmented Lagrangian and ADMM type algorithm is straightforward but new. Convergence results of the new randomized variation for non-convex problems are also novel, to my best knowledge. Despite the notable originality, I think a couple of places need to be further discussed or clarified. Although existing work on nonconvex SVRG/SAGA algorithms [1,21] only provide analysis for smooth problems, I would presume similar results (replacing gradient by prox-gradient) can also be derived with slight modification given that the original algorithms are designed to handle nonsmooth regularization and adapted to non-uniform sampling as well. So it would be good if the author could add such comparison to nonconvex SVRG/SAGA in Table 1 when applicable. 2. It appears to me that in the NESTT-G algorithm (without reducing to the single variable form), at each iteration, setting the remaining (N-1) x variables to z would require O(Nd) computation and memory cost, which is not negligible.