We propose a novel neural algorithm for the fundamental problem of computing the entropic optimal transport (EOT) plan between 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：我们提出一种新的神经算法,以解决在样本可获取的概率分布之间计算最优化载运(EOT)计划的根本问题。我们的算法基于重塑“EOT”动态版本的支撑点,即所谓的“Schr\'odinger桥”问题。 与以往的大规模EOT方法相比,我们的算法是端到端的,由单一学习步骤组成,具有快速推论程序,并允许处理在有些应用问题中特别重要的酶规范系数的微值。我们经常地展示该方法在若干大规模 EOT任务上的性能。