mlsanityData to 14 Oct 2026

Convergence Rates for Regularized Optimal Transport via Quantization

arXiv 2208.14391 ↗First posted 30 Aug 2022math.OC math.PR stat.MLcited by 12

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Abstract (arXiv)

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 multi-marginal problems are obtained. A novel methodology using quantization and martingale couplings is suitable for non-compact marginals and achieves, in particular, the sharp leading-order term of entropically regularized 2-Wasserstein distance for all marginals with finite (2+δ)-moment.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 23 of its 63 references that are in the map. First posted on arXiv 30 Aug 2022.

Builds on

23 of 63 references.

References · 23

  1. 2013Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distancescited by 2,316
  2. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 292
  3. 2014On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpointcited by 99
  4. 2021Entropic estimation of optimal transport mapscited by 90
  5. 2017Smooth and Sparse Optimal Transportcited by 83
  6. 2019On Efficient Optimal Transport: An Analysis of Greedy and Accelerated Mirror Descent Algorithmscited by 62
  7. 2014Multi-marginal optimal transport: theory and applicationscited by 41
  8. 2021Entropic Optimal Transport: Convergence of Potentialscited by 31
  9. 2021Stability of Entropic Optimal Transport and Schr"odinger Bridgescited by 26
  10. 2018An explicit analysis of the entropic penalty in linear programmingcited by 24
  11. 2021Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithmcited by 22
  12. 2021Entropic Optimal Transport: Geometry and Large Deviationscited by 20
11 more
  1. 2017Quadratically-Regularized Optimal Transport on Graphscited by 19
  2. 2019Quadratically regularized optimal transportcited by 15
  3. 2020Polynomial-time algorithms for Multimarginal Optimal Transport problems with structurecited by 15
  4. 2021Asymptotics for semi-discrete entropic optimal transportcited by 14
  5. 2022Stability of Schr"odinger Potentials and Convergence of Sinkhorn's Algorithmcited by 13
  6. 2022Computational methods for adapted optimal transportcited by 12
  7. 2018Towards Optimal Running Times for Optimal Transportcited by 11
  8. 2020Optimal Transport losses and Sinkhorn algorithm with general convex regularizationcited by 10
  9. 2017Generalized incompressible flows, multi-marginal transport and Sinkhorn algorithmcited by 9
  10. 2022Convergence rate of general entropic optimal transport costscited by 9
  11. 2021Optimal transport with f-divergence regularization and generalized Sinkhorn algorithmcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 7; 2024: 2; 2025: 1; 2026: 2.

12 papers.

  1. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  2. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
  3. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  4. 2023Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithmcited by 10
  5. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  6. 2023Estimating the Rate-Distortion Function by Wasserstein Gradient Descentcited by 5
  7. 2023Fitted value iteration methods for bicausal optimal transportcited by 2
  8. 2024Multivariate Stochastic Dominance via Optimal Transport and Applications to Models Benchmarkingcited by 2
  9. 2025Statistical Inference for Optimal Transport Maps: Recent Advances and Perspectivescited by 1
  10. 2023Convergence rate of Tsallis entropic regularized optimal transportcited by 0
  11. 2026Quadratically Regularized Optimal Transport: Localization Bounds and Affine Case Analysiscited by 0
  12. 2026Randomized Optimal Switching Problem and Related Mirror Descent Flowcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023On a Relation Between the Rate-Distortion Function and Optimal Transport
  2. 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transport
  3. 2021Improving Approximate Optimal Transport Distances using Quantization
  4. 2026Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities
  5. 2024Optimal Rates of Convergence for Entropy Regularization in Discounted Markov Decision Processes
  6. 2025Quantization-based Bounds on the Wasserstein Metric
  7. 2023Soft Quantization using Entropic Regularization
  8. 2026The Geometry Behind Diffusion and Flow Matching: Gradient Flows and Geodesics in Wasserstein Space