标题： 从优化角度设计熵最优运输的算法 显示英文标题

标题： Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective

摘要： 在本工作中，我们开发了一套新的方法用于熵正则化最优传输问题，这些方法受到用于解决该问题的Sinkhorn算法现有镜像下降解释的启发。 这些方法从根本上是从优化的角度提出的：要么基于相关的半对偶问题，要么基于在联合分布子集上求解非凸约束问题。 这种优化观点在对问题结构的最小假设下，为所提出的方法提供了非渐近的收敛速率。 我们还通过这种观点提出了一种配备动量的方法，具有可证明的加速保证，类似于欧几里得设置中的情况。 我们基于联合分布上的优化所开发的更广泛的框架，在动态Schrödinger桥问题中也找到了类似的对应关系。 显示英文摘要

摘要： In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are fundamentally proposed from an optimisation perspective: either based on the associated semi-dual problem, or based on solving a non-convex constrained problem over subset of joint distributions. This optimisation viewpoint results in non-asymptotic rates of convergence for the proposed methods under minimal assumptions on the problem structure. We also propose a momentum-equipped method with provable accelerated guarantees through this viewpoint, akin to those in the Euclidean setting. The broader framework we develop based on optimisation over the joint distributions also finds an analogue in the dynamical Schr\"{o}dinger bridge problem.