Learning to Transport with Neural Networks

08/04/2019

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by   Andrea Schioppa, et al.

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12

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We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: "Heuristics" and approaches with a more sound mathematical justification, motivated by the dual of the Kantorovitch problem. Among the algorithms we consider a novel approach involving dynamic flows and reductions of Optimal Transport to supervised learning.