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.

翻译：我们针对连续概率分布间熵最优传输（EOT）计划计算这一基础问题提出了一种新颖的神经网络算法，该算法仅需通过样本即可访问分布。我们的方法基于EOT动态版本（即薛定谔桥问题）的鞍点重表述。与先前大规模EOT方法不同，本算法是端到端的，仅需单步学习，具有快速推理过程，且能够处理熵正则化系数较小的情况——这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任务中展现了出色性能。