Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective

Vishwak Srinivasan, Qijia Jiang
Proceedings of The 37th International Conference on Algorithmic Learning Theory, PMLR 313:1-33, 2026.

Abstract

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{ö}dinger bridge problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v313-srinivasan26a, title = {Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective}, author = {Srinivasan, Vishwak and Jiang, Qijia}, booktitle = {Proceedings of The 37th International Conference on Algorithmic Learning Theory}, pages = {1--33}, year = {2026}, editor = {Telgarsky, Matus and Ullman, Jonathan}, volume = {313}, series = {Proceedings of Machine Learning Research}, month = {23--26 Feb}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v313/main/assets/srinivasan26a/srinivasan26a.pdf}, url = {https://proceedings.mlr.press/v313/srinivasan26a.html}, abstract = {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{ö}dinger bridge problem.} }
Endnote
%0 Conference Paper %T Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective %A Vishwak Srinivasan %A Qijia Jiang %B Proceedings of The 37th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Matus Telgarsky %E Jonathan Ullman %F pmlr-v313-srinivasan26a %I PMLR %P 1--33 %U https://proceedings.mlr.press/v313/srinivasan26a.html %V 313 %X 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{ö}dinger bridge problem.
APA
Srinivasan, V. & Jiang, Q.. (2026). Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective. Proceedings of The 37th International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 313:1-33 Available from https://proceedings.mlr.press/v313/srinivasan26a.html.

Related Material