Before revision: We present a first-order algorithm for nonconvex-nonconcave min-max optimization problems such as those that arise in training GANs . Our algorithm provably converges in time polynomial in the dimension and smoothness parameters of the loss function .
After revision: We present a first-order algorithm for nonconvex-nonconcave min-max framework for GANs to learn a distribution, where the discriminator can update its strategy in a greedy manner until it reaches a first-order stationary point. We give an algorithm to train such a GAN and show that it provably converges from any initial point to an approximate local equilibrium for this framework . Our algorithm provably converges in time polynomial in the dimension and smoothness parameters of the loss function .