In this paper, we present a new formulation of unbalanced optimal transport called Dual Regularized Optimal Transport (DROT). We argue that regularizing the dual formulation of optimal transport results in a version of unbalanced optimal transport that leads to sparse solutions and that gives us control over mass creation and destruction. We build intuition behind such control and present theoretical properties of the solutions to DROT. We demonstrate that due to recent advances in optimization techniques, we can feasibly solve such a formulation at large scales and present extensive experimental evidence for this formulation and its solution.

翻译：在本文中,我们提出了一种不平衡的最佳运输方式的新提法,称为“双常规最佳运输方式(DROT) ” ( DROT ) 。 我们主张,将最佳运输方式的双重提法正规化,形成一种不平衡的最佳运输方式,导致产生稀少的解决办法,并使我们能够控制大规模创造和破坏。我们建立这种控制背后的直觉,并介绍DROT解决方案的理论特性。 我们证明,由于最近在优化技术方面取得的进步,我们可以大范围切实解决这种提法,并为这种提法及其解决方案提供广泛的实验证据。