Splitting algorithms for training GANs

Generative adversarial networks (GANs) are an approach to fitting generative models over complex structured spaces. Within this framework, the fitting problem is posed as a zero-sum game between two competing neural networks which are trained simultaneously. Mathematically, this problem takes the form of a saddle-point problem; a well-known example of the type of problem where the usual (stochastic) gradient descent-type approaches used for training neural networks fail. In this talk, we rectify this shortcoming by proposing a new method for training GANs that has: (i) a sounds theoretical foundation, and (ii) does not increase the algorithm's per iteration complexity (as compared to gradient descent). The theoretical analysis is performed within the framework of monotone operator splitting.