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.
@article{arxiv.1908.01394,
title = {Learning to Transport with Neural Networks},
author = {Andrea Schioppa},
journal= {arXiv preprint arXiv:1908.01394},
year = {2019}
}