Learning to Transport with Neural Networks
This work addresses the challenge of efficient optimal transport computation for machine learning applications, presenting incremental improvements in method design.
The paper tackles the problem of learning an optimal transport map between probability distributions using neural networks, comparing heuristic methods with mathematically justified approaches based on the Kantorovitch dual and introducing a novel method using dynamic flows and supervised learning reductions.
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.