mlsanityData to 14 Oct 2026

Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm

arXiv 2110.06798 ↗First posted 13 Oct 2021math.OC math.AP math.PRcited by 22

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Abstract (arXiv)

We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H"older continuity of the optimal coupling in p-Wasserstein distance are obtained under general conditions including quadratic costs and unbounded marginals. The results for the value extend to regularization by an arbitrary divergence. As an application, we show convergence of Sinkhorn's algorithm in Wasserstein sense, including for quadratic cost. Two techniques are presented: The first compares an optimal coupling with its so-called shadow, a coupling induced on other marginals by an explicit construction. The second transforms one set of marginals by a change of coordinates and thus reduces the comparison of differing marginals to the comparison of differing cost functions under the same marginals.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Oct 2021.

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Citing papers per year: 2022: 4; 2023: 7; 2024: 4; 2025: 2; 2026: 5.

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  1. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  2. 2022Convergence Rates for Regularized Optimal Transport via Quantizationcited by 12
  3. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  4. 2024Progressive Entropic Optimal Transport Solverscited by 10
  5. 2022Distributional Reinforcement Learning with Regularized Wasserstein Losscited by 8
  6. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  7. 2023Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approachcited by 7
  8. 2023Efficient and Accurate Optimal Transport with Mirror Descent and Conjugate Gradientscited by 7
  9. 2024Optimal Transport on the Lie Group of Roto-translationscited by 4
  10. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
  11. 2023On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detectioncited by 3
  12. 2024Fast Tree-Field Integrators: From Low Displacement Rank to Topological Transformerscited by 3
10 more
  1. 2023Fitted value iteration methods for bicausal optimal transportcited by 2
  2. 2022Stability of Entropic Wasserstein Barycenters and application to random geometric graphscited by 1
  3. 2026On the Expressive Power of Transformers for Contextual Relationscited by 1
  4. 2023Convergence rate of Tsallis entropic regularized optimal transportcited by 0
  5. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  6. 2025Robust Optimization in Causal Models and G-Causal Normalizing Flowscited by 0
  7. 2026QDSB: Quantized Diffusion Schr"odinger Bridgescited by 0
  8. 2026Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parametercited by 0
  9. 2026General Quantification of Covariate and Concept Shiftscited by 0
  10. 2026Scaling Online Optimal Transport Minibatches for Flow Matchingcited by 0