  Training generative adversarial networks (GANs) often suffers from cyclic
behaviors of iterates. Based on a simple intuition that the direction of
centripetal acceleration of an object moving in uniform circular motion is
toward the center of the circle, we present the Simultaneous Centripetal
Acceleration (SCA) method and the Alternating Centripetal Acceleration (ACA)
method to alleviate the cyclic behaviors. Under suitable conditions, gradient
descent methods with either SCA or ACA are shown to be linearly convergent for
bilinear games. Numerical experiments are conducted by applying ACA to existing
gradient-based algorithms in a GAN setup scenario, which demonstrate the
superiority of ACA.
