📋 摘要
⭐ 画像为空，按通用ML读者打分；优化算法学习化方向有理论与实验，质量中等。
Learning Over-Relaxation Policies for ADMM with Convergence Guarantees
中文
本文研究在结构化凸优化中广泛使用的 Alternating Direction Method of Multipliers (ADMM) 的参数选择问题，特别关注 penalty 与 relaxation 参数对实际收敛性能的影响。针对 Model Predictive Control (MPC) 等需反复求解结构固定、仅参数变化的相关优化问题的应用场景，作者提出在线学习 relaxation 参数更新策略的思路，以在感兴趣的问题类上提升求解效率。该设计在 OSQP-like 架构中具有计算优势：调整 relaxation 不会像更新 penalty 那样触发矩阵重新分解 (matrix refactorization)。在方法层面，作者在温和假设下建立了具有时变 penalty 与 relaxation 参数的 ADMM 的收敛性保证 (convergence guarantees)，从理论上支撑了学习型策略的可靠性。在实验层面，作者在标准 quadratic programs 基准问题上验证所学策略，结果显示相较于 baseline OSQP，所学习的 over-relaxation policy 在迭代次数和 wall-clock time 上均有改善。与现有工作不同之处在于：本文将可学习的 relaxation 在线更新与时变参数下的 ADMM 收敛性分析相结合，从而在保持理论保证的同时获得实际加速。
English abstract
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, and show on benchmark quadratic programs that the resulting learned policies improve both iteration count and wall-clock time over baseline OSQP.
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