发表机构
Sun Yat-sen University（中山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对二部图上二次正则化最优传输问题，提出分布式加速预条件ADMM（DAP-ADMM），实现全局收敛与非遍历O(1/k)界，并通过无求解器投影和自适应惩罚机制加速收敛。
AI 中文摘要
最优传输（OT）在机器学习、经济学和管理学中有着广泛的应用。然而，经典OT模型并不直接适用于具有图结构连通性和不平衡质量的分配问题。二部图上的分布式OT公式满足了这些需求，但通常通过ADMM求解，其收敛速度慢限制了通信效率。我们将加速预条件ADMM（AP-ADMM）应用于二次正则化的分布式OT模型，并开发了DAP-ADMM，这是一种完全分布式的算法，其中每个节点仅与其图邻居通信。对于固定的局部惩罚参数，我们建立了全局收敛性以及KKT残差范数和原始目标间隙的非遍历$O(1/k)$界。我们为局部ADMM子问题中出现的区间约束投影推导了一种精确的无求解器例程。我们提出了一种分布式自适应惩罚机制，该机制使用局部可计算的KKT残差分量更新节点特定惩罚，而无需全局聚合。数值实验证实了无求解器例程的效率以及DAP-ADMM相对于标准分布式ADMM的实际加速效果。
英文摘要
Optimal transport (OT) has found broad applications in machine learning, economics, and management. Classical OT models, however, are not directly suited to allocation problems with graph-structured connectivity and unbalanced mass. Distributed OT formulations on bipartite graphs address these requirements but are typically solved by ADMM, whose slow convergence limits communication efficiency. We adapt the accelerated preconditioned ADMM (AP-ADMM) to the quadratically regularized distributed OT model and develop DAP-ADMM, a fully distributed algorithm in which each node communicates only with its graph neighbors. For fixed local penalty parameters, we establish global convergence and non-ergodic $O(1/k)$ bounds for both the KKT-residual norm and the primal objective gap. We derive an exact solver-free routine for the interval-constrained projections arising in the local ADMM subproblems. We propose a distributed self-adaptive penalty mechanism that updates node-specific penalties using locally computable KKT-residual components without global aggregation. Numerical experiments confirm the efficiency of the solver-free routine and the practical acceleration of DAP-ADMM over standard distributed ADMM.
