Before revision:  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. Empirically, GANs trained using our algorithm consistently learn a greater number of modes than gradient descent-ascent (GDA), optimistic mirror descent (OMD), andunrolled GANs when applied to a synthetic Gaussian mixture dataset. Moreover, they perform significantly better on CIFAR-10 than OMD and GDA when comparing the mean and standard deviation of the Inception Score respectively .
After revision:  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 arise in GAN training. Our algorithm converges on these test functions and, when used to train GANs on synthetic and real-world datasets, trains stably and avoids mode collapse .