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Convergence Rates for Regularized Optimal Transport via Quantization

Author

Listed:
  • Stephan Eckstein

    (Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland)

  • Marcel Nutz

    (Departments of Statistics and Mathematics, Columbia University, New York, New York 10027)

Abstract

We study the convergence of divergence-regularized optimal transport as the regularization parameter vanishes. Sharp rates for general divergences including relative entropy or L p 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 + δ ) -moment.

Suggested Citation

  • Stephan Eckstein & Marcel Nutz, 2024. "Convergence Rates for Regularized Optimal Transport via Quantization," Mathematics of Operations Research, INFORMS, vol. 49(2), pages 1223-1240, May.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:2:p:1223-1240
    DOI: 10.1287/moor.2022.0245
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