Efficient second-order optimization with predictions in differential games

A growing number of training methods for generative adversarial networks (GANs) are differential games. Different from convex optimization problems on single functions, gradient descent on multiple objectives may not converge to stable fixed points (SFPs). In order to improve learning dynamics in such games, many recently proposed methods utilize the second-order information of the game, such as the Hessian matrix. Unfortunately, these methods often suffer from the enormous computational cost of Hessian, which hinders their further applications. In this paper, we present efficient second-order optimization (ESO), in which only a part of Hessian is updated in each iteration, and the algorithm is derived. Furthermore, we give the local convergence of the method under reasonable assumptions. In order to further speed up the training process of GANs, we propose efficient second-order optimization with predictions (ESOP) using a novel accelerator. Basic experiments show that the proposed learning methods are faster than some state-of-art methods in GANs, while applicable to many other n-player differential games with local convergence guarantee.