通过学习动态调整松弛参数，提升ADMM求解效率并保证收敛。
Learning Over-Relaxation Policies for ADMM with Convergence Guarantees
- 学习在线更新松弛参数，避免矩阵重分解，计算更高效。
- 在基准二次规划问题上，迭代次数和实际运行时间均优于基线方法。
- 适用于重复求解结构相似、参数变化的优化问题，如模型预测控制。
交替方向乘子法（ADMM）是求解结构化凸优化的常用方法，其实际性能高度依赖于惩罚项和松弛参数的选择。针对模型预测控制（MPC）等场景中需反复求解结构固定但参数变化的优化问题，本文提出学习在线更新松弛参数的方法，以提升特定问题类别的求解性能。该策略在类似OSQP的架构中具有计算优势，因松弛参数调整无需触发与惩罚项更新相关的矩阵重分解。在弱假设下建立了含时变惩罚与松弛参数的ADMM收敛性理论，并在基准二次规划问题上验证：所学策略显著降低迭代次数与实际运行时间，优于基线OSQP。
原文摘要 · Abstract (English)
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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