  We reconsider the training objective of Generative Adversarial Networks
(GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the
classical prox methods, we develop a novel algorithmic framework for GANs via
an infinite-dimensional two-player game and prove rigorous convergence rates to
the mixed NE, resolving the longstanding problem that no provably convergent
algorithm exists for general GANs. We then propose a principled procedure to
reduce our novel prox methods to simple sampling routines, leading to
practically efficient algorithms. Finally, we provide experimental evidence
that our approach outperforms methods that seek pure strategy equilibria, such
as SGD, Adam, and RMSProp, both in speed and quality.
