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.
After revision:  Our algorithm runs in time polynomial in the dimension, our algorithm is first-order and its iteration bound is independent of dimension. We empirically evaluate our algorithm on challenging nonconvex-nonconcave test-functions and loss functions that can be nonconvex and nonconcave in the parameters of the generator and discriminator.