Entropic Neural Optimal Transport via Diffusion Processes

• URL: http://arxiv.org/abs/2211.01156v3
• Date: Wed, 1 Nov 2023 13:46:27 GMT
• Title: Entropic Neural Optimal Transport via Diffusion Processes
• Authors: Nikita Gushchin, Alexander Kolesov, Alexander Korotin, Dmitry Vetrov, Evgeny Burnaev
• Abstract summary: We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous probability distributions. Our algorithm is based on the saddle point reformulation of the dynamic version of EOT which is known as the Schr"odinger 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.
• Score: 105.34822201378763
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between continuous 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 Schr\"odinger 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. https://github.com/ngushchin/EntropicNeuralOptimalTransport

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