Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909691612758016 |
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| author | Srinivasan, Vishwak Jiang, Qijia |
| author_facet | Srinivasan, Vishwak Jiang, Qijia |
| contents | 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 Schrödinger bridge problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_12246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective Srinivasan, Vishwak Jiang, Qijia Optimization and Control Probability Machine Learning 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 Schrödinger bridge problem. |
| title | Designing Algorithms for Entropic Optimal Transport from an Optimisation Perspective |
| topic | Optimization and Control Probability Machine Learning |
| url | https://arxiv.org/abs/2507.12246 |