mlsanityData to 13 Oct 2026

Stability of Entropic Optimal Transport and Schr"odinger Bridges

arXiv 2106.03670 ↗First posted 7 Jun 2021math.OC math.AP math.FAcited by 25

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Abstract (arXiv)

We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the use of c-cyclical monotonicity in classical optimal transport. As a consequence of stability, we obtain the wellposedness of the solution in this geometric sense, even when all transports have infinite cost. More generally, our results apply to a class of static Schr"odinger bridge problems including entropic optimal transport.

Key facts. Cited by 25 papers in the map (data through 13 Oct 2026). First posted on arXiv 7 Jun 2021.

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 2; 2022: 3; 2023: 4; 2024: 5; 2025: 5; 2026: 6.

25 papers.

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  1. 2021Entropic estimation of optimal transport mapscited by 88
  2. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  3. 2023Minimax estimation of discontinuous optimal transport maps: The semi-discrete casecited by 20
  4. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  5. 2024Identifying Drift, Diffusion, and Causal Structure from Temporal Snapshotscited by 12
  6. 2021Quantitative Uniform Stability of the Iterative Proportional Fitting Procedurecited by 11
  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. 2024Progressive Entropic Optimal Transport Solverscited by 10
  10. 2025Momentum Multi-Marginal Schr"odinger Bridge Matchingcited by 9
  11. 2024Plug-in estimation of Schr"odinger bridgescited by 8
  12. 2024Feedback Schr"odinger Bridge Matchingcited by 4
13 more
  1. 2024A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithmcited by 4
  2. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  3. 2025Weighted Conditional Flow Matchingcited by 3
  4. 2026The Amazing Stability of Flow Matchingcited by 2
  5. 2025Distributionally Robust Deep Q-Learningcited by 1
  6. 2025RadioFlow: Efficient Radio Map Construction Framework with Flow Matchingcited by 1
  7. 2026Generalized Schr"odinger Bridge on Graphscited by 1
  8. 2026Exploring and Exploiting Stability in Latent Flow Matchingcited by 1
  9. 2023Stochastic optimal transport in Banach Spaces for regularized estimation of multivariate quantilescited by 0
  10. 2025Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavitycited by 0
  11. 2026Sinkhorn Linearization and the Spectral Proxy: Unifying the Statistical and Algorithmic Theory of Feature-Parameterized Inverse Optimal Transport via a Single Spectral Sandwichcited by 0
  12. 2026EMS Coreset: An Efficient Expectation-Maximization Algorithm for Sinkhorn Coresetcited by 0
  13. 2026Uniform Statistical Convergence of Empirical Sinkhorn Potentials with Exponential and Polynomial Dependence on the Regularization Parametercited by 0