Fast and Provable ADMM for Learning with Generative Priors
This addresses optimization challenges in tasks like compressive sensing and adversarial robustness for researchers and practitioners using generative priors, though it is incremental as it adapts ADMM to a specific constraint type.
The paper tackles the problem of minimizing convex functions with nonconvex constraints from neural network ranges, proposing a linearized ADMM algorithm that is faster and handles non-smooth objectives better than gradient descent, with rates proven under mild assumptions for feedforward architectures.
In this work, we propose a (linearized) Alternating Direction Method-of-Multipliers (ADMM) algorithm for minimizing a convex function subject to a nonconvex constraint. We focus on the special case where such constraint arises from the specification that a variable should lie in the range of a neural network. This is motivated by recent successful applications of Generative Adversarial Networks (GANs) in tasks like compressive sensing, denoising and robustness against adversarial examples. The derived rates for our algorithm are characterized in terms of certain geometric properties of the generator network, which we show hold for feedforward architectures, under mild assumptions. Unlike gradient descent (GD), it can efficiently handle non-smooth objectives as well as exploit efficient partial minimization procedures, thus being faster in many practical scenarios.