Sliced-Regularized Optimal Transport

arXiv stat.ML / 4/28/2026

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Key Points

The paper introduces a new regularized optimal transport method called sliced-regularized optimal transport (SROT), which improves classical OT by using a smoothed sliced OT (SOT) plan as the regularization reference instead of the independence coupling used in entropic OT (EOT).
The authors provide a formal SROT definition, derive its dual formulation, and offer a post-Bayesian interpretation, connecting the method to probabilistic reasoning.
They develop a Sinkhorn-style algorithm that keeps the scalability benefits of EOT while enabling more accurate approximation of the exact OT plan at the same regularization level.
The work also defines an SROT-induced OT divergence (SROT divergence) and analyzes its topological and computational properties, showing experimentally stronger performance than EOT and SOT on both approximation and gradient-flow-related tasks.

Abstract

We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a smoothened sliced OT (SOT) plan. To the best of our knowledge, SROT is the first approach to leverage a version of SOT plan as a reference to improve classical OT. We provide a formal definition of SROT, derive its dual formulation, and provide a post-Bayesian interpretation of SROT. We then develop a Sinkhorn-style algorithm for efficient computation, retaining the same scalability advantages as EOT. By incorporating a scalable SOT plan as a prior, SROT yields more accurate approximations of the exact OT plan than EOT under the same level of regularization. Moreover, the resulting transport plan improves upon the reference SOT plan itself. We further introduce the corresponding OT divergence induced by SROT, named SROT divergence, and analyze its topological and computational properties. Finally, we validate our approach through experiments on synthetic datasets and color transfer tasks, demonstrating that SROT is better than both EOT and SOT in approximating exact OT. Additional experiments on gradient flows further highlight the advantages of SROT divergence.