Learning to Transport with Neural Networks

2019/08/04 by Andrea Schioppa, Schioppa, Andrea
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Computer science #Dual (grammatical number) #FOS: Computer and information sciences #Heuristics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Machine learning #Mathematical optimization #Mathematics #Model Reduction and Neural Networks #Neural Networks and Applications #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1908.01394

published in arXiv (Cornell University) (Cornell University)

arxiv created 2019/08/04 · openalex publication_date 2019/08/04 · arxiv updated 2019/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

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.

Citations

• Stochastic Optimization for Large-scale Optimal Transport
• Towards Principled Methods for Training Generative Adversarial Networks

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