mlsanityData to 7 Oct 2026

Entropic Optimal Transport: Geometry and Large Deviations

arXiv 2102.04397 ↗First posted 8 Feb 2021math.OC math.FA math.PRcited by 20

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Abstract (arXiv)

We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the local exponential convergence rate as the regularization parameter vanishes. The exact rate function is determined in a general setting and linked to the Kantorovich potential of optimal transport. Our arguments are based on the geometry of the optimizers and inspired by the use of c-cyclical monotonicity in classical transport theory. The results can also be phrased in terms of Schr"odinger bridges.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Feb 2021.

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Citing papers per year: 2021: 5; 2022: 3; 2023: 6; 2024: 1; 2025: 4; 2026: 1.

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  1. 2021Entropic estimation of optimal transport mapscited by 87
  2. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  3. 2022On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Errorcited by 16
  4. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  5. 2021Quantitative Uniform Stability of the Iterative Proportional Fitting Procedurecited by 11
  6. 2022Convergence Rates for Regularized Optimal Transport via Quantizationcited by 11
  7. 2023Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithmcited by 10
  8. 2023Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithmcited by 8
  9. 2021Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transportcited by 5
  10. 2024Iterated Schr"odinger bridge approximation to Wasserstein Gradient Flowscited by 5
  11. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  12. 2023On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detectioncited by 3
8 more
  1. 2025ContextFlow: Context-Aware Flow Matching For Trajectory Inference From Spatial Omics Datacited by 2
  2. 2021Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applicationscited by 1
  3. 2021Estimation of Stationary Optimal Transport Planscited by 0
  4. 2023Convergence rate of Tsallis entropic regularized optimal transportcited by 0
  5. 2025Scalable Approximate Algorithms for Optimal Transport Linear Modelscited by 0
  6. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  7. 2025Langevin Diffusion Approximation to Same Marginal Schr"odinger Bridgecited by 0
  8. 2026Reflected Schr"odinger Bridge Matchingcited by 0