Neural Optimal Transport with General Cost Functionals

Arip Asadulaev, Alexander Korotin, Vage Egiazarian, Evgeny Burnaev

Keywords: Optimal Transport, Neural Networks, Generative Modelling, Unpaired Learning

Abstract: We present a novel neural-networks-based algorithm to compute optimal transport (OT) plans and maps for general cost functionals. The algorithm is based on a saddle point reformulation of the OT problem and generalizes prior OT methods for weak and strong cost functionals. As an application, we construct a functional to map data distributions with preserving the class-wise structure of data.

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