About the analogy between optimal transport and minimal entropy

By Ivan Gentil, Christian Léonard, Luigia Ripani. 2015

95 citations recorded by the source corpus.

We describe some analogy between optimal transport and the Schr\"odinger problem where the transport cost is replaced by an entropic cost with a reference path measure. A dual Kantorovich type formulation and a Benamou-Brenier type representation formula of the entropic cost are derived, as well as contraction inequalities with respect to the entropic cost. This analogy is also illustrated with some numerical examples where the reference path measure is given by the Brownian or the Ornstein-Uhlenbeck process. Our point of view is measure theoretical and the relative entropy with respect to path measures plays a prominent role.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f64b9ce3a264322a8d020b095abbdcd6d0ed5f17

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Time reversal of diffusion processes under a finite entropy condition (2021, methodology): “To give some examples, in [4] and [17] a fluid-dynamic (Benamou-Brenier) formulation of entropic optimal transport is derived leveraging time reversal arguments, and similar ideas are also used in [2] in a mean field setting.”
A formula for the time derivative of the entropic cost and applications (2019, background): “The fluid-dynamical formulation of the entropic cost [7, 14, 18, 33] asserts that, at least under (H4), we have”