  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.
