Reviews: Online ICA: Understanding Global Dynamics of Nonconvex Optimization via Diffusion Processes

This paper aims to study the global dynamics of nonconvex statistical optimization based on diffusion processes. As an example of non-convex problems, this paper discusses in details the SGD applied on the tensor decomposition formulation of independent component analysis (ICA). An interesting finding in this paper is a three-phases phenomenon of the global dynamics of SGD to capture the transition of SGD solution from unstable initialization to finally stable local minimum. Overall, this paper is well written and it addresses a very challenge problem. This paper serves as a first step in the theoretical understanding of global dynamics of SGD, and is believed to stimulate many work on the global dynamic of non-convex optimizations. Q1: Discuss how to generalize it other non-convex models?