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SGD Learns One-Layer Networks in WGANs

Qi Lei · Jason Lee · Alexandros Dimakis · Constantinos Daskalakis

Keywords: [ Computational Learning Theory ] [ Deep Learning Theory ] [ Non-convex Optimization ] [ Optimization - Non-convex ]


Generative adversarial networks (GANs) are a widely used framework for learning generative models. Wasserstein GANs (WGANs), one of the most successful variants of GANs, require solving a minmax optimization problem to global optimality, but are in practice successfully trained using stochastic gradient descent-ascent. In this paper, we show that, when the generator is a one-layer network, stochastic gradient descent-ascent converges to a global solution with polynomial time and sample complexity.

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