# Entropic Optimal Transport: Geometry and Large Deviations

arXiv: https://arxiv.org/abs/2102.04397 · HTML: https://mlsanity.com/paper/2102.04397/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2021.

## Built on by (most cited first, 20 of 20)

- [Entropic estimation of optimal transport maps](https://mlsanity.com/paper/2109.12004/) (2021)
- [Minimax estimation of discontinuous optimal transport maps: The semi-discrete case](https://mlsanity.com/paper/2301.11302/) (2023)
- [On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Error](https://mlsanity.com/paper/2202.03618/) (2022)
- [Convergence Rates for Regularized Optimal Transport via Quantization](https://mlsanity.com/paper/2208.14391/) (2022)
- [Lower Complexity Adaptation for Empirical Entropic Optimal Transport](https://mlsanity.com/paper/2306.13580/) (2023)
- [Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure](https://mlsanity.com/paper/2108.08129/) (2021)
- [Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm](https://mlsanity.com/paper/2307.16421/) (2023)
- [Hilbert's projective metric for functions of bounded growth and exponential convergence of Sinkhorn's algorithm](https://mlsanity.com/paper/2311.04041/) (2023)
- [Nearly Tight Convergence Bounds for Semi-discrete Entropic Optimal Transport](https://mlsanity.com/paper/2110.12678/) (2021)
- [Iterated Schr"odinger bridge approximation to Wasserstein Gradient Flows](https://mlsanity.com/paper/2406.10823/) (2024)
- [Wasserstein Distributionally Robust Optimization with Wasserstein Barycenters](https://mlsanity.com/paper/2203.12136/) (2022)
- [On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detection](https://mlsanity.com/paper/2302.07964/) (2023)
- [ContextFlow: Context-Aware Flow Matching For Trajectory Inference From Spatial Omics Data](https://mlsanity.com/paper/2510.02952/) (2025)
- [Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applications](https://mlsanity.com/paper/2107.13494/) (2021)
- [Estimation of Stationary Optimal Transport Plans](https://mlsanity.com/paper/2107.11858/) (2021)
- [Convergence rate of Tsallis entropic regularized optimal transport](https://mlsanity.com/paper/2304.06616/) (2023)
- [Scalable Approximate Algorithms for Optimal Transport Linear Models](https://mlsanity.com/paper/2504.04609/) (2025)
- [Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity](https://mlsanity.com/paper/2504.11133/) (2025)
- [Langevin Diffusion Approximation to Same Marginal Schr"odinger Bridge](https://mlsanity.com/paper/2505.07647/) (2025)
- [Reflected Schr"odinger Bridge Matching](https://mlsanity.com/paper/2607.03626/) (2026)

## 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.