Multiple marginal matching problem aims at learning mappings to match a source domain to multiple target domains and it has attracted great attention in many applications, such as multi-domain image translation. However, addressing this problem has two critical challenges: (i) Measuring the multi-marginal distance among different domains is very intractable; (ii) It is very difficult to exploit cross-domain correlations to match the target domain distributions. In this paper, we propose a novel Multi-marginal Wasserstein GAN (MWGAN) to minimize Wasserstein distance among domains. Specifically, with the help of multi-marginal optimal transport theory, we develop a new adversarial objective function with inner- and inter-domain constraints to exploit cross-domain correlations. Moreover, we theoretically analyze the generalization performance of MWGAN, and empirically evaluate it on the balanced and imbalanced translation tasks. Extensive experiments on toy and real-world datasets demonstrate the effectiveness of MWGAN.

本文中提出了一种新的多重边际Wasserstein GAN（MWGAN）来最小化域之间的Wasserstein距离，并利用多边际最优传输理论开发了一种新的对抗性目标函数以利用交叉域相关性，并在平衡和不平衡的翻译任务上进行了理论分析和实验证明了MWGAN的有效性。

多边沃瑟斯坦生成对抗网络