Before revision:  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 runs in time polynomial in the smoothness parameters of the loss function and independent of the dimension, and allows for loss functions that can be nonconvex and nonconcave in the parameters of the generator and discriminator.
After revision:  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 our framework from any initialization and for nonconvex-nonconcave loss functions. Compared to the second-order algorithm of Mangoubi and Vishnoi, whose iteration bound is polynomial in the smoothness parameters of the loss function and independent of the dimension, and allows for loss functions that can be nonconvex and nonconcave in the parameters of the generator and discriminator.