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

翻译：我们提出了一种新颖的神经算法，用于解决通过样本可访问的连续概率分布之间计算熵最优传输（EOT）计划这一基本问题。该算法基于EOT动态版本的鞍点重新表述，即著名的薛定谔桥问题。与现有大规模EOT方法不同，我们的算法具有端到端特性，仅包含单一学习步骤，具备快速推理流程，并能够处理熵正则化系数较小的情形——该特性在某些应用问题中尤为重要。实验表明，该方法在多个大规模EOT任务中展现出良好性能。https://github.com/ngushchin/EntropicNeuralOptimalTransport