论文标题
Minmax最佳运输及以后的方法：正则化，近似和数字
MinMax Methods for Optimal Transport and Beyond: Regularization, Approximation and Numerics
论文作者
论文摘要
我们研究了Minmax解决方案方法，用于与最佳运输有关的一般优化问题。从理论上讲，重点是将大量的问题纳入一个Minmax框架，并从经典的最佳运输中概括正则化技术。我们表明，正则化技术证明了神经网络通过证明近似定理的利用来解决此类问题，并说明如果不使用正则化，则说明了基本问题。我们进一步研究了与生成对抗网的文献的关系，并分析其中使用的算法技术特别适合本文研究的一系列问题。几个数值实验展示了设置的一般性，并突出了哪些理论见解在实践中最有益。
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing regularization techniques known from classical optimal transport. We show that regularization techniques justify the utilization of neural networks to solve such problems by proving approximation theorems and illustrating fundamental issues if no regularization is used. We further study the relation to the literature on generative adversarial nets, and analyze which algorithmic techniques used therein are particularly suitable to the class of problems studied in this paper. Several numerical experiments showcase the generality of the setting and highlight which theoretical insights are most beneficial in practice.
