Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assumption of convex-concavity, guided by a continuous-time analysis with differential equations. First, we show that simGD, as is, converges with stochastic sub-gradients under strict convexity in the primal variable. Second, we generalize optimistic simGD to accommodate an optimism rate separate from the learning rate and show its convergence with full gradients. Finally, we present anchored simGD, a new method, and show convergence with stochastic subgradients.

翻译：尽管取得了显著的成功,但基因对抗网络(GAN)的培训动态(GAN)涉及使用随机梯度解决迷你马克斯游戏,其培训动态仍然鲜为人知。在这项工作中,我们分析了同时的梯度下降(simGD)及其变体在以差异方程的连续时间分析为指导的假设下,同时的梯度下降(simGD)及其变体的最后程度趋同。首先,我们显示SimGD与原始变量严格相近的随机次等级相趋同。第二,我们普及了乐观的模拟GD,以适应与学习率分开的乐观率,并显示其与完全梯度的趋同。最后,我们介绍了固定的模拟GD(一种新方法),并展示了与随机次等级的趋同。