STABILITY OF SCHRODINGER POTENTIALS AND CONVERGENCE OF SINKHORN'S ALGORITHM

• 成果类型: Article
• 署名作者: Nutz, Marcel; Wiesel, Johannes
• 署名单位: Columbia University; Columbia University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1611
• 发表日期: 2023
• 页码: 699-722
• 关键词: Matrices

摘要

We study the stability of entropically regularized optimal transport with respect to the marginals. Given marginals converging weakly, we establish a strong convergence for the Schr delta dinger potentials, describing the density of the optimal couplings. When the marginals converge in total variation, the optimal couplings also converge in total variation. This is applied to show that Sinkhorn's algorithm converges in total variation when costs are quadratic and marginals are subgaussian or, more generally, for all continuous costs satisfying an integrability condition.