INDIVIDUAL COMMENTS / QUESTIONS 1) I really appreciate how the paper ties up loose ends by unifying the analysis of several momentum-based methods in the stochastic setting. I am not very closely familiar with the literature analyzing momentum methods, but there's a lot of work out there (e.g., the line of research studying momentum methods in the continuous time limit). A brief review would be very helpful to position the paper within the existing work. To me this implies that the analysis would go through for more general functions. I don't find it obvious that it would.

In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable to nonconvex as well as convex functions. Moreover, the framework permits the use of noise-corrupted gradients, as well as first-order approximations to the gradient (sometimes referred to as "gradient-free" approaches). By viewing the analysis of the iterations as a problem in the convergence of stochastic processes, we are able to establish a very general theorem, which includes most known convergence results for zeroth-order and first-order methods. The analysis of "second-order" or momentum-based methods is not a part of this paper, and will be studied elsewhere. However, numerical experiments indicate that momentum-based methods can fail if the true gradient is replaced by its first-order approximation. This requires further theoretical analysis.