发表机构
Hanoi University of Science and Technology; High School for the Gifted; VinUniversity; Rochambeau French International School; RMIT University; Aalto University; Linköping University（河内理工大学; 天才高中; VinUniversity; 罗尚博法语国际学校; 皇家墨尔本理工大学; 阿尔托大学; 林雪平大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于惩罚重述的加速一阶算法，利用平滑强凸正则化器生成稀疏部分最优传输计划，在颜色迁移、域适应和点云配准中实现更低成本、更高稀疏性和更快收敛。
AI 中文摘要
部分最优传输（POT）通过放宽严格的质量守恒约束来扩展经典最优传输问题，使其能够应用于广泛的现实世界场景。在许多此类应用中，稀疏传输计划因其可解释性和计算优势而受到青睐。尽管平滑且强凸的正则化器（如二次或弹性网络）已在各种机器学习应用中被广泛用于诱导稀疏性和加速计算，但在计算POT方面，与熵方法相比，它们受到的算法关注较少。在本文中，我们提出了一种新的优化框架，通过基于惩罚的重新表述利用这些正则化器，从而在保持原始问题结构的同时实现高效的基于梯度的更新。我们的方法适用于一大类促进结构化稀疏传输计划的正则化器。基于此表述，我们设计了一种加速的一阶算法，该算法在平滑更新和简单投影步骤之间交替进行。通过在颜色迁移、域适应和点云配准上的实证基准测试，我们的方法始终优于现有基线——实现更低的传输成本、更高的稀疏性和更快的收敛速度——使其成为现代传输问题的实用且可扩展的解决方案。
英文摘要
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.
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