Entropic Neural Optimal Transport via Diffusion Processes

Nikita Gushchin, Alexander Kolesov, Alexander Korotin, Dmitry P. Vetrov, Evgeny Burnaev

Keywords: Optimal transport, Schrödinger Bridge, Entropy regularized OT, Neural Networks, Unpaired Learning

Abstract: We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between probability distributions which are accessible by samples. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schrödinger Bridge problem. In contrast to the prior methods for large-scale EOT, our algorithm is end-to-end and consists of a single learning step, has fast inference procedure, and allows handling small values of the entropy regularization coefficient which is of particular importance in some applied problems. Empirically, we show the performance of the method on several large-scale EOT tasks. The code for the ENOT solver can be found at https://github.com/ngushchin/EntropicNeuralOptimalTransport

Submission Number: 3529