# Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective

arXiv: https://arxiv.org/abs/2507.12246 · HTML: https://mlsanity.com/paper/2507.12246/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 16 Jul 2025.

## Builds on (most cited first, 22 of 22)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Wasserstein Proximal Algorithms for the Schr"odinger Bridge Problem: Density Control with Nonlinear Drift](https://mlsanity.com/paper/1912.01244/) (2019)
- [An Optimal Transport approach for the Schr"odinger bridge problem and convergence of Sinkhorn algorithm](https://mlsanity.com/paper/1911.06850/) (2019)
- [On the Efficiency of Entropic Regularized Algorithms for Optimal Transport](https://mlsanity.com/paper/1906.01437/) (2019)
- [Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EM](https://mlsanity.com/paper/2206.08873/) (2022)
- [Entropic Optimal Transport: Convergence of Potentials](https://mlsanity.com/paper/2104.11720/) (2021)
- [Semi-dual Regularized Optimal Transport](https://mlsanity.com/paper/1811.05527/) (2018)
- [A gradient descent perspective on Sinkhorn](https://mlsanity.com/paper/2002.03758/) (2020)
- [Projected Langevin dynamics and a gradient flow for entropic optimal transport](https://mlsanity.com/paper/2309.08598/) (2023)
- [A fast approach to optimal transport: The back-and-forth method](https://mlsanity.com/paper/1905.12154/) (2019)
- [Schr"odinger Bridge Samplers](https://mlsanity.com/paper/1912.13170/) (2019)
- [Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm](https://mlsanity.com/paper/2307.16421/) (2023)
- [Sharper Exponential Convergence Rates for Sinkhorn's Algorithm in Continuous Settings](https://mlsanity.com/paper/2407.01202/) (2024)
- [Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent](https://mlsanity.com/paper/1909.06918/) (2019)
- [A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm](https://mlsanity.com/paper/2412.09235/) (2024)

## Abstract (arXiv)

In this work, we develop a collection of novel methods for the entropic-regularised optimal transport problem, which are inspired by existing mirror descent interpretations of the Sinkhorn algorithm used for solving this problem. These are fundamentally proposed from an optimisation perspective: either based on the associated semi-dual problem, or based on solving a non-convex constrained problem over subset of joint distributions. This optimisation viewpoint results in non-asymptotic rates of convergence for the proposed methods under minimal assumptions on the problem structure. We also propose a momentum-equipped method with provable accelerated guarantees through this viewpoint, akin to those in the Euclidean setting. The broader framework we develop based on optimisation over the joint distributions also finds an analogue in the dynamical Schr"odinger bridge problem.