Learning context-aware adaptive solvers to accelerate quadratic programming

TL;DR

This paper introduces CA-ADMM, a novel adaptive solver that learns to adjust the step-size parameter in ADMM for quadratic programming, significantly improving convergence speed by leveraging spatio-temporal context during optimization.

Contribution

It proposes a context-aware learning approach to dynamically tune ADMM parameters, enhancing its efficiency across diverse quadratic programming problems.

Findings

CA-ADMM outperforms traditional methods in convergence speed.

It generalizes well to unseen QP problem sizes and structures.

Dynamic adjustment of  improves optimization efficiency.

Abstract

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 $\rho$. Due to the absence of a general rule for setting $\rho$, it is often tuned manually or heuristically. In this paper, we propose CA-ADMM (Context-aware Adaptive ADMM)) which learns to adaptively adjust $\rho$ 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 $\rho$ 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 $\rho$ considering the stage of the optimization process to accelerate the convergence speed further.