Wasserstein Generative Adversarial Networks (WGANs) provide a versatile class
of models, which have attracted great attention in various applications.
However, this framework has two main drawbacks: (i) Wasserstein-1 (or
Earth-Mover) distance is restrictive such that WGANs cannot always fit data
geometry well; (ii) It is difficult to achieve fast training of WGANs. In this
paper, we propose a new class of \textit{Relaxed Wasserstein} (RW) distances by
generalizing Wasserstein-1 distance with Bregman cost functions. We show that
RW distances achieve nice statistical properties while not sacrificing the
computational tractability. Combined with the GANs framework, we develop
Relaxed WGANs (RWGANs) which are not only statistically flexible but can be
approximated efficiently using heuristic approaches. Experiments on real images
demonstrate that the RWGAN with Kullback-Leibler (KL) cost function outperforms
other competing approaches, e.g., WGANs, even with gradient penalty.

本文提出了一种新的 Relaxed Wasserstein（RW）距离，通过广义化 Wasserstein-1 距离与 BregmanCost 函数，其所得到的 RW 距离具有良好的统计性能，同时不牺牲计算可行性，与 GANs 框架结合，我们开发了 Relaxed WGANs（RWGANs），在使用启发式方法进行近似的同时不仅在统计上具有灵活性，而且在现实图像上的实验表明，在使用 KL 代价函数下，RWGAN 优于其他竞争方法，例如 WGAN，即使使用梯度惩罚。