A geometric perspective on regularized optimal transport

Abstract

We present new geometric intuition on dynamical versions of regularized optimal transport. We introduce two families of variational problems on Riemannian manifolds which contain analogues of the Schrödinger bridge problem and the Yasue problem. We also propose an analogue of the Hopf--Cole transformation in the geometric setting.

arXiv commentAdded more details in Section 4.2. as well as minor improvements

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