Generative Adversarial Networks (GANs) are one of the most practical strategies to learn data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions. Unfortunately, minimizing the Wasserstein distance between the data distribution and the generative model distribution is a challenging problem as its objective is non-convex, non-smooth, and even hard to compute. In this work, we propose to use a smooth approximation of the Wasserstein GANs. We show that this smooth approximation is close to the original objective. Moreover, obtaining gradient information of this approximate formulation is computationally effortless and hence one can easily apply first order optimization methods to optimize this objective. Based on this observation, we proposed a class of algorithms with guaranteed theoretical convergence to stationarity. Unlike the original non-smooth objective, our proposed algorithm only requires solving the discriminator to approximate optimality. We applied our method to learning Gaussian mixtures on a grid and also to learning MNIST digits. Our method allows the use of powerful cost functions based on latent representations of the data, where this latent representation could also be optimized adversarially.

本文通过基于正则化最优传输的平滑Wasserstein GAN公式实现梯度信息的获取，从而实现对该目标函数的一阶优化，为一类生成对抗网络优化算法建立了理论收敛保证，且仅需要解决鉴别器问题以近似最优。该算法计算效率高，应用于MNIST数字以及CIFAR-10图像数据集相比其他同等架构和计算能力的算法生成的图像效果显著。

使用正则化最优传输训练 GAN 的收敛性和鲁棒性