mlsanityData to 14 Oct 2026

An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithm

arXiv 1911.06850 ↗First posted 15 Nov 2019math.PR math.OCcited by 38

Not on the map. Why?

Abstract (arXiv)

This paper exploit the equivalence between the Schr"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a priori estimates which are consistent in the limit when the regularization parameter goes to zero. In particular, we find a new proof of the existence of maximizing entropic-potentials and therefore, the existence of a solution of the Schr"odinger system. Our method extends also when we have more than two marginals: we can provide an alternative proof of the convergence of the Sinkhorn algorithm with two marginals and we show that the Sinkhorn algorithm converges in the multi-marginal case.

Key facts. Cited by 38 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Nov 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 3; 2023: 11; 2024: 7; 2025: 7; 2026: 4.

38 papers.

Sort:

By area:

  1. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  2. 2022Trajectory Inference via Mean-field Langevin in Path Spacecited by 30
  3. 2023Energy-guided Entropic Neural Optimal Transportcited by 26
  4. 2022The Multimarginal Optimal Transport Formulation of Adversarial Multiclass Classificationcited by 21
  5. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  6. 2023Tree-Based Diffusion Schr"odinger Bridge with Applications to Wasserstein Barycenterscited by 16
  7. 2021On the complexity of the optimal transport problem with graph-structured costcited by 14
  8. 2024Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Priorcited by 13
  9. 2025DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignmentcited by 13
  10. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  11. 2023Energy-Guided Continuous Entropic Barycenter Estimation for General Costscited by 12
  12. 2024Reflected Schr"odinger Bridge for Constrained Generative Modelingcited by 12
26 more
  1. 2023Minimum intrinsic dimension scaling for entropic optimal transportcited by 11
  2. 2023Doubly Regularized Entropic Wasserstein Barycenterscited by 10
  3. 2023Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approachcited by 7
  4. 2024Annealed Sinkhorn for Optimal Transport: convergence, regularization path and debiasingcited by 7
  5. 2024An Optimal Transport Approach for Computing Adversarial Training Lower Bounds in Multiclass Classificationcited by 5
  6. 2025On the Hopf-Cole Transform for Control-affine Schr"odinger Bridgecited by 5
  7. 2021Optimal transport with f-divergence regularization and generalized Sinkhorn algorithmcited by 4
  8. 2021Matching for causal effects via multimarginal unbalanced optimal transportcited by 4
  9. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
  10. 2025Gradient-flow SDEs have unique transient population dynamicscited by 4
  11. 2023On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detectioncited by 3
  12. 2023On the Contraction Coefficient of the Schr"odinger Bridge for Stochastic Linear Systemscited by 3
  13. 2023Path Structured Multimarginal Schr"odinger Bridge for Probabilistic Learning of Hardware Resource Usage by Control Softwarecited by 3
  14. 2024Stochastic Learning of Computational Resource Usage as Graph Structured Multimarginal Schr"odinger Bridgecited by 3
  15. 2025Entropic optimal transport beyond product reference couplings: the Gaussian case on Euclidean spacecited by 2
  16. 2025Optimal Multimarginal Schr"odinger Bridge: Minimum Spanning Tree over Measure-valued Verticescited by 1
  17. 2026New Trends in the Stability of Sinkhorn Semigroupscited by 1
  18. 2026Robust Sublinear Convergence Rates for Iterative Bregman Projectionscited by 1
  19. 2021Estimation of Stationary Optimal Transport Planscited by 0
  20. 2021Convergence of Batch Greenkhorn for Regularized Multimarginal Optimal Transportcited by 0
  21. 2022Metric Distribution to Vector: Constructing Data Representation via Broad-Scale Discrepanciescited by 0
  22. 2024Inverse Entropic Optimal Transport Solves Semi-supervised Learning via Data Likelihood Maximizationcited by 0
  23. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  24. 2025Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspectivecited by 0
  25. 2026Generative Profiling for Soft Real-Time Systems and its Applications to Resource Allocationcited by 0
  26. 2026Optimal and Scalable MAPF via Multi-Marginal Optimal Transport and Schr"odinger Bridgescited by 0