DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee

TL;DR

This paper introduces DPOT, a deep learning method for computing optimal transport maps from unpaired samples, with theoretical convergence guarantees and demonstrated effectiveness on real-world data.

Contribution

It presents a novel deep particle-based approach for optimal transport that guarantees convergence without restrictions on network structure.

Findings

The method achieves accurate transport maps in experiments.

Theoretical convergence and error bounds are established.

Effective on real-world datasets.

Abstract

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min optimization during training and does not impose any restriction on the network structure. Theoretically we establish a weak convergence guarantee and a quantitative error bound between the learned map and the optimal transport map. Our numerical experiments validate the theoretical results and the effectiveness of the new approach, particularly on real-world tasks.