Accelerated Algorithm for Sparse Regularized Partial Optimal Transport

2026-09-30

AI Summary

This study addresses the computational inefficiency of existing partial optimal transport (POT) methods in inducing sparse transport plans and their difficulty in accommodating non-entropic regularizers. We propose a novel penalty-based optimization framework that, for the first time, introduces smooth strongly convex regularizations—such as quadratic or elastic net penalties—into POT to accelerate computation. By reformulating the problem via penalization, the framework preserves the original structure while supporting a broad class of structured sparsity-inducing regularizers. Furthermore, we design an accelerated first-order algorithm that alternates between gradient updates and projection steps, enabling efficient large-scale optimization. Experimental results demonstrate that the proposed method significantly reduces transport costs in tasks such as color transfer while substantially improving sparsity and convergence speed. Overall, it outperforms existing baselines and exhibits strong scalability.

Abstract

Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use in a wide range of real-world applications. In many of these settings, sparse transport plans are preferred for their interpretability and computational benefits. While smooth and strongly convex regularizers - such as quadratic or elastic net - have been vastly used in various machine learning applications to induce sparsity and accelerate computation, they have received less algorithmic attention compared to entropic approaches for computational POT. In this paper, we propose a new optimization framework that leverages these regularizers through a penalty-based reformulation, enabling efficient gradient-based updates while preserving the structure of the original problem. Our method accommodates a broad class of regularizers that promote structured and sparse transport plans. Building on this formulation, we design an accelerated first-order algorithm that alternates between smooth updates and simple projection steps. Through empirical benchmarks on color transfer, domain adaptation, and point cloud registration, our approach consistently outperforms established baselines - achieving lower transport cost, higher sparsity, and faster convergence - making it a practical and scalable solution for modern transport problems.

Problem

• Partial Optimal Transport
• Sparse Regularization
• Transport Plan
• Penalty-based Reformulation

Innovation

• Partial Optimal Transport
• Sparse Regularization
• Accelerated First-Order Algorithm
• Penalty-Based Reformulation
• Optimal Transport