Convergence Rates for Regularized Optimal Transport via Quantization

• 成果类型: Article; Early Access
• 署名作者: Eckstein, Stephan; Nutz, Marcel
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2022.0245
• 发表日期: 2023
• 关键词: large-deviations; barycenters; FLOWS; MAPS

摘要

We study the convergence of divergence-regularized optimal transport as the regularization 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.