论文标题
正规化最佳运输是地面成本对手
Regularized Optimal Transport is Ground Cost Adversarial
论文作者
论文摘要
正式化最佳运输（OT）问题已证明对OT理论影响机器学习领域至关重要。例如，众所周知，与经典OT相比，使用sindhorn算法将OT问题正规化会导致更快的计算和更好的分化样品复杂性界限。在这项工作中，我们从这个实际的角度出发，并提出了对正则化的新解释，并使用Fenchel二元性表明，OT的任何凸正则化都可以解释为地面成本对抗性。偶然地，可以访问地面空间上强大的差异度量，而该度量又可以在其他应用中使用。我们建议算法来计算这种稳健的成本，并以经验说明这种方法的兴趣。
Regularizing the optimal transport (OT) problem has proven crucial for OT theory to impact the field of machine learning. For instance, it is known that regularizing OT problems with entropy leads to faster computations and better differentiation using the Sinkhorn algorithm, as well as better sample complexity bounds than classic OT. In this work we depart from this practical perspective and propose a new interpretation of regularization as a robust mechanism, and show using Fenchel duality that any convex regularization of OT can be interpreted as ground cost adversarial. This incidentally gives access to a robust dissimilarity measure on the ground space, which can in turn be used in other applications. We propose algorithms to compute this robust cost, and illustrate the interest of this approach empirically.
