Reviews: Fast and Provable ADMM for Learning with Generative Priors

I think the "global optimization" aspect of the main result and the fast (i.e., linear) convergence rate are very interesting, and perhaps also surprising. For example, for the least square problem min_z A G(z) - b prior works such as Hand & Voroninski [2017] and Heckel et al [2019] have established the global optimization aspect of simple gradient descent like algorithms. But the result obtained in this paper is much more general, and also applies to formulations with extra nonsmooth terms, with a practical numerical method. Moreover, general understanding of ADMM applied to nonconvex problems is still very rare. I think this result is definitely a beautiful addition to this line of literature also.