Entropic Optimal Transport between (Unbalanced) Gaussian Measures has a Closed Form

3 Jun 2020Hicham JanatiBoris MuzellecGabriel PeyréMarco Cuturi

Although optimal transport (OT) problems admit closed form solutions in a very few notable cases, e.g. in 1D or between Gaussians, these closed forms have proved extremely fecund for practitioners to define tools inspired from the OT geometry. On the other hand, the numerical resolution of OT problems using entropic regularization has given rise to many applications, but because there are no known closed-form solutions for entropic regularized OT problems, these approaches are mostly algorithmic, not informed by elegant closed forms... (read more)

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