On the Linear Convergence of the Multimarginal Sinkhorn Algorithm
本文给出了多边际最优传输熵正则化问题中Sinkhorn算法线性收敛性的一个初等证明，适用于一般概率空间，对研究最优传输和算法收敛性的学者有参考价值。
The aim of this note is to give an elementary proof of linear convergence of the Sinkhorn algorithm for the entropic regularization of multimarginal optimal transport in the setting of general probability spaces. The proof simply relies on (i) the fact that Sinkhorn iterates are bounded, (ii) the strong convexity of the exponential on bounded intervals, and (iii) the convergence analysis of the coordinate descent (Gauss--Seidel) method of Beck and Tetruashvili [SIAM J. Optim, 23 (2013), pp. 2037--2060].