Learning context-aware adaptive solvers to accelerate quadratic programming
This work addresses a bottleneck in optimization for researchers and practitioners using ADMM, offering an incremental improvement over existing methods.
The paper tackles the problem of slow convergence in ADMM for quadratic programming due to manual step-size tuning, proposing CA-ADMM which learns to adaptively adjust the step-size based on spatio-temporal context, resulting in effective generalization to unseen QP problems and accelerated convergence.
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.