论文标题
学习上下文感知的自适应求解器，以加速二次编程
Learning context-aware adaptive solvers to accelerate quadratic programming
论文作者
论文摘要
凸二次编程（QP）是数学优化的重要子场。乘数的交替方向方法（ADMM）是解决QP的成功方法。尽管ADMM在解决各种QP方面显示出令人鼓舞的结果，但已知其收敛速度高度依赖于阶梯尺寸的参数$ρ$。由于缺乏设置$ρ$的一般规则，因此通常是手动或启发式调整的。在本文中，我们提出了CA-ADMM（上下文感知的自适应ADMM）），该）学会了适应性地调整$ρ$以加速ADMM。 CA-ADMM提取时空上下文，该上下文捕获了QP的原始变量和双重变量及其在ADMM迭代期间的时间演变的依赖性。 CA-ADMM根据提取的上下文选择$ρ$。通过广泛的数值实验，我们验证了CA-ADMM有效地概括了具有不同大小和类别（即具有不同QP参数结构）的QP问题。此外，我们验证了CA-ADMM可以动态调整$ρ$，考虑到优化过程的阶段以进一步加速收敛速度。
Convex quadratic programming (QP) is an important sub-field of mathematical optimization. The alternating direction method of multipliers (ADMM) is a successful method to solve QP. Even though ADMM shows promising results in solving various types of QP, its convergence speed is known to be highly dependent on the step-size parameter $ρ$. Due to the absence of a general rule for setting $ρ$, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust $ρ$ to accelerate ADMM. CA-ADMM extracts the spatio-temporal context, which captures the dependency of the primal and dual variables of QP and their temporal evolution during the ADMM iterations. CA-ADMM chooses $ρ$ based on the extracted context. Through extensive numerical experiments, we validated that CA-ADMM effectively generalizes to unseen QP problems with different sizes and classes (i.e., having different QP parameter structures). Furthermore, we verified that CA-ADMM could dynamically adjust $ρ$ considering the stage of the optimization process to accelerate the convergence speed further.
