  This paper mainly conducts further research to alleviate the issue of limit
cycling behavior in training generative adversarial networks (GANs) through the
proposed predictive centripetal acceleration algorithm (PCAA). Specifically, we
first derive the upper and lower bounds on the last-iterate convergence rates
of PCAA for the general bilinear game, with the upper bound notably improving
upon previous results. Then, we combine PCAA with the adaptive moment
estimation algorithm (Adam) to propose PCAA-Adam, a practical approach for
training GANs. Finally, we validate the effectiveness of the proposed algorithm
through experiments conducted on bilinear games, multivariate Gaussian
distributions, and the CelebA dataset, respectively.
