Entropic Neural Optimal Transport via Diffusion Processes
This addresses the need for efficient and scalable algorithms for entropic optimal transport, which is a fundamental problem in machine learning with applications in areas like generative modeling and domain adaptation, though it appears incremental as it builds on prior dynamic EOT methods.
The paper tackles the problem of computing entropic optimal transport (EOT) plans between continuous probability distributions using samples, proposing a neural algorithm based on the Schrödinger Bridge problem. The result is an end-to-end method with fast inference and the ability to handle small entropy regularization coefficients, demonstrated empirically on large-scale EOT tasks.
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 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. https://github.com/ngushchin/EntropicNeuralOptimalTransport