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.

翻译：本文主要开展进一步研究，通过提出的预测向心加速度算法（PCAA）缓解生成对抗网络（GAN）训练中的极限环行为。具体而言，我们首先推导了PCAA在一般双线性博弈中最终迭代收敛速率的上下界，其中上界显著优于此前结果。随后，我们将PCAA与自适应矩估计算法（Adam）结合，提出PCAA-Adam这一训练GAN的实用方法。最后，我们通过在双线性博弈、多元高斯分布和CelebA数据集上分别开展的实验，验证了所提算法的有效性。