mlsanityData to 13 Oct 2026

Entropic Optimal Transport: Convergence of Potentials

arXiv 2104.11720 ↗First posted 23 Apr 2021math.AP math.FA math.OCcited by 30

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Abstract (arXiv)

We study the potential functions that determine the optimal density for varepsilon-entropically regularized optimal transport, the so-called Schr"odinger potentials, and their convergence to the counterparts in classical optimal transport, the Kantorovich potentials. In the limit varepsilon→0 of vanishing regularization, strong compactness holds in L1 and cluster points are Kantorovich potentials. In particular, the Schr"odinger potentials converge in L1 to the Kantorovich potentials as soon as the latter are unique. These results are proved for all continuous, integrable cost functions on Polish spaces. In the language of Schr"odinger bridges, the limit corresponds to the small-noise regime.

Key facts. Cited by 30 papers in the map (data through 13 Oct 2026). First posted on arXiv 23 Apr 2021.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 6; 2024: 5; 2025: 8; 2026: 4.

30 papers.

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  1. 2021Entropic estimation of optimal transport mapscited by 88
  2. 2023LAVA: Data Valuation without Pre-Specified Learning Algorithmscited by 69
  3. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  4. 2026One-Step Generative Modeling via Wasserstein Gradient Flowscited by 20
  5. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  6. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  7. 2022Convergence Rates for Regularized Optimal Transport via Quantizationcited by 11
  8. 2023Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithmcited by 10
  9. 2024Conditional simulation via entropic optimal transport: Toward non-parametric estimation of conditional Brenier mapscited by 9
  10. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  11. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  12. 2021Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transportcited by 5
18 more
  1. 2021Matching for causal effects via multimarginal unbalanced optimal transportcited by 4
  2. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
  3. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  4. 2024Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasetscited by 3
  5. 2025Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysiscited by 2
  6. 2023Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithmcited by 1
  7. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  8. 2025Hierarchical Maximum Entropy via the Renormalization Groupcited by 1
  9. 2026Geometric Regularization for Long-Tailed Semi-Supervised Learning via Gaussian Feature Bridgescited by 1
  10. 2021Estimation of Stationary Optimal Transport Planscited by 0
  11. 2024Semi-Discrete Optimal Transport: Nearly Minimax Estimation With Stochastic Gradient Descent and Adaptive Entropic Regularizationcited by 0
  12. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  13. 2025Langevin Diffusion Approximation to Same Marginal Schr"odinger Bridgecited by 0
  14. 2025Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspectivecited by 0
  15. 2025E-ROBOT: a dimension-free method for robust statistics and machine learning via Schr"odinger bridgecited by 0
  16. 2025Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transportcited by 0
  17. 2026Multimodal Alignment Through Joint Kernel Entropic Gromov--Wasserstein Optimal Transportcited by 0
  18. 2026Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parametercited by 0