In this work we undertake a thorough study of the non-asymptotic properties of the vanilla generative adversarial networks (GANs). We prove an oracle inequality for the Jensen-Shannon (JS) divergence between the underlying density $\mathsf{p}^*$ and the GAN estimate with a significantly better statistical error term compared to the previously known results. The advantage of our bound becomes clear in application to nonparametric density estimation. We show that the JS-divergence between the GAN estimate and $\mathsf{p}^*$ decays as fast as $(\log{n}/n)^{2\beta/(2\beta + d)}$, where $n$ is the sample size and $\beta$ determines the smoothness of $\mathsf{p}^*$. This rate of convergence coincides (up to logarithmic factors) with minimax optimal for the considered class of densities.

翻译：本文对标准生成对抗网络（GANs）的非渐近性质进行了深入研究。我们证明了底层密度$\mathsf{p}^*$与GAN估计之间的Jensen-Shannon (JS)散度存在一个oracle不等式，其统计误差项显著优于先前已知结果。该界限的优势在非参数密度估计应用中尤为明显。研究表明，GAN估计与$\mathsf{p}^*$之间的JS散度的衰减速率达到$(\log{n}/n)^{2\beta/(2\beta + d)}$，其中$n$为样本量，$\beta$决定$\mathsf{p}^*$的光滑性。该收敛速率（至多相差对数因子）与所考虑密度类别的极小化最优速率一致。