We formulate the training of generative adversarial networks (GANs) as a Nash equilibrium seeking problem. To stabilize the training process and find a Nash equilibrium, we propose an asymmetric regularization mechanism based on the classic Tikhonov step and on a novel zero-centered gradient penalty. Under smoothness and a local identifiability condition induced by a Gauss-Newton Gramian, we obtain explicit Lipschitz and (strong)-monotonicity constants for the regularized operator. These constants ensure last-iterate linear convergence of a single-call Extrapolation-from-the-Past (EFTP) method. Empirical simulations on an academic example show that, even when strong monotonicity cannot be achieved, the asymmetric regularization is enough to converge to an equilibrium and stabilize the trajectory.

翻译：本文将生成对抗网络（GAN）的训练问题表述为纳什均衡求解问题。为稳定训练过程并找到纳什均衡，我们提出一种基于经典吉洪诺夫步长与新型零中心梯度惩罚的非对称正则化机制。在由高斯-牛顿格拉姆矩阵诱导的光滑性及局部可辨识性条件下，我们推导出正则化算子的显式利普希茨常数与（强）单调性常数。这些常数保证了单次调用"过去外推法"（EFTP）具有末点线性收敛性。在学术算例上的实证模拟表明，即使无法达成强单调性条件，非对称正则化机制仍足以收敛至均衡点并稳定训练轨迹。