  The traditional approach of hand-crafting priors (such as sparsity) for
solving inverse problems is slowly being replaced by the use of richer learned
priors (such as those modeled by generative adversarial networks, or GANs). In
this work, we study the algorithmic aspects of such a learning-based approach
from a theoretical perspective. For certain generative network architectures,
we establish a simple non-convex algorithmic approach that (a) theoretically
enjoys linear convergence guarantees for certain inverse problems, and (b)
empirically improves upon conventional techniques such as back-propagation. We
also propose an extension of our approach that can handle model mismatch (i.e.,
situations where the generative network prior is not exactly applicable.)
Together, our contributions serve as building blocks towards a more complete
algorithmic understanding of generative models in inverse problems.
