Can we optimize and learn in nonconvex-nonconcave game?

In this talk I will focus of the problem of GAN training. As a researcher in optimization and machine learning, my goal is to find a training method that achieve high performance (learning a 'good' generator) and solves the minimax nonconvex-nonconcave optimization problem (finds a stationary point for optimizer). We will see that, quite unexpectedly, there seems to be a tension between solving the learning problem and solving the optimization problem. We will then investigate from an optimization perspective which methods are actually able to solve the learning problem.