DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee
This work addresses a fundamental challenge in machine learning for applications like data alignment and generative modeling, offering a novel approach with proven guarantees.
The authors tackled the problem of computing optimal transport maps between continuous distributions using unpaired samples, achieving a method with theoretical convergence guarantees and validated effectiveness in numerical experiments.
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.