Convergence Rates for Regularized Optimal Transport via Quantization br

• 成果类型: Article
• 署名作者: Eckstein, Stephan; Nutz, Marcel
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• 发表日期: 2024
• 页码: 1223-1240
• 关键词: secretary problem

摘要

We study the convergence of divergence-regularized optimal transport as the reg-ularization parameter vanishes. Sharp rates for general divergences including relative entropy or Lp regularization, general transport costs, and multimarginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for noncompact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for marginals with a finite (2+delta)-moment.