Generative Adversarial Networks (GANs) have become a popular method to learn a probability model from data. Many GAN architectures with different optimization metrics have been introduced recently. Instead of proposing yet another architecture, this paper aims to provide an understanding of some of the basic issues surrounding GANs. First, we propose a natural way of specifying the loss function for GANs by drawing a connection with supervised learning. Second, we shed light on the generalization peformance of GANs through the analysis of a simple LQG setting: the generator is Linear, the loss function is Quadratic and the data is drawn from a Gaussian distribution. We show that in this setting: 1) the optimal GAN solution converges to population Principal Component Analysis (PCA) as the number of training samples increases; 2) the number of samples required scales exponentially with the dimension of the data; 3) the number of samples scales almost linearly if the discriminator is constrained to be quadratic. Thus, linear generators and quadratic discriminators provide a good balance for fast learning.

本文研究了生成对抗网络在高维高斯数据下的建模、鲁棒性以及泛化能力，并提出了一种能快速推广、拥有全局稳定性的 GAN 结构模型，最终利用模型设计实现了 GAN 在复杂数据下的应用。

理解GANs: LQG设置