[论文] Learning Over-Relaxation Policies for ADMM with Convergence Guarantees

论文概要

研究领域: ML 作者: Junan Lin, Paul J. Goulart, Luca Furieri 发布时间: 2025-04-30 arXiv: 2504.20813

中文摘要

乘子交替方向法（ADMM）是结构化凸优化中广泛使用的方法，其实际性能高度依赖于惩罚参数和松弛参数的选择。受模型预测控制（MPC）等场景的启发——在这些场景中需要反复求解结构固定但参数变化的优化问题——我们提出学习松弛参数的在线更新策略，以提升在感兴趣问题类别上的性能。这一选择在类OSQP架构中具有计算优势，因为调整松弛参数不会触发与惩罚参数更新相关的矩阵重构。我们在温和假设下建立了时变惩罚和松弛参数ADMM的收敛保证，并在基准二次规划上展示了所得学习策略相比基线OSQP在迭代次数和 wall-clock 时间上的双重改进。

原文摘要

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such as Model Predictive Control (MPC), where one repeatedly solves related optimization problems with fixed structure and changing parameter values, we propose learning online updates of the relaxation parameter to improve performance on problem classes of interest. This choice is computationally attractive in OSQP-like architectures, since adapting relaxation does not trigger the matrix refactorizations associated with penalty updates. We establish convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions, a...

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