论文标题
在固定高斯工艺的矩匹配gan的纳什平衡下
On the Nash equilibrium of moment-matching GANs for stationary Gaussian processes
论文作者
论文摘要
生成对抗网络（GAN）通过两人游戏从数据样本中学习隐式生成模型。在本文中，我们研究了游戏的NASH平衡存在，随着数据样本的数量增长到无穷大。在一个可实现的环境中，目标是估计固定高斯过程的基础真相发生器，我们表明，NASH平衡的存在的存在至关重要取决于歧视家族的选择。根据二阶统计矩定义的歧视器可能会导致NASH平衡不存在，存在一致的非NASH平衡，或者存在和一致的NASH平衡的存在和独特性，这取决于是否尊重发电机家族的对称性。我们从经验上进一步研究了梯度下降方法对一致平衡的局部稳定性和全球收敛性。
Generative Adversarial Networks (GANs) learn an implicit generative model from data samples through a two-player game. In this paper, we study the existence of Nash equilibrium of the game which is consistent as the number of data samples grows to infinity. In a realizable setting where the goal is to estimate the ground-truth generator of a stationary Gaussian process, we show that the existence of consistent Nash equilibrium depends crucially on the choice of the discriminator family. The discriminator defined from second-order statistical moments can result in non-existence of Nash equilibrium, existence of consistent non-Nash equilibrium, or existence and uniqueness of consistent Nash equilibrium, depending on whether symmetry properties of the generator family are respected. We further study empirically the local stability and global convergence of gradient descent-ascent methods towards consistent equilibrium.
