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.

Source code is made available at https://github.com/ymLeiFDU/LICO.

We develop a deeper understanding of its relationship with more conventional analyses of extragradient methods [Nem04, Nes07]. We also give improved solvers for the subproblems required by variants of the [She17] algorithm, designed through the lens of relative smoothness [BBT17, LFN18].

Work completed at the University of Washington. Work completed at Microsoft Research.

Two salient limitations have long hindered the relevance of optimal transport methods to machine learning.

Our novel setup brings new understandings to both disentanglement and equivariance .