Sliced-Regularized Optimal Transport

2026-04-26

AI Summary

This work addresses the inherent bias of entropic optimal transport (EOT) in approximating exact solutions, which struggles to balance computational efficiency and accuracy. We propose Smoothed Sliced Regularized Optimal Transport (SROT), a novel framework that, for the first time, incorporates sliced optimal transport (SOT) plans as structured priors within a regularization scheme, yielding a theoretically sound and practically effective paradigm. We define the corresponding SROT divergence and, leveraging dual formulation and a Bayesian posterior interpretation, design a Sinkhorn-like iterative algorithm that seamlessly integrates the strengths of both SOT and classical OT. Experiments demonstrate that, under identical regularization strength, SROT achieves more accurate approximations of exact OT than EOT and SOT on synthetic data and color transfer tasks, with gradient flow results further corroborating its superiority.

Technology Category

• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Data transparency and provenance
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• optimal transport
• regularization
• sliced optimal transport
• transport plan approximation
• OT divergence

Innovation

• Sliced-Regularized Optimal Transport
• Optimal Transport
• Entropic Regularization
• Sliced Optimal Transport
• Sinkhorn Algorithm