A Learning-Based Inexact ADMM for Solving Quadratic Programs

TL;DR

This paper presents a neural-accelerated inexact ADMM method for quadratic programs that maintains convergence guarantees and significantly speeds up solving times while improving solution accuracy.

Contribution

It introduces a learning-based inexact ADMM variant using LSTM networks, with proven convergence guarantees and superior empirical performance.

Findings

Achieves up to 28x speedup over existing solvers.

Maintains primal-dual convergence with learned approximations.

Outperforms existing learning-based methods in solution quality.

Abstract

Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has emerged as a preferred first-order approach due to its iteration efficiency - exemplified by the state-of-the-art OSQP solver. Machine learning-enhanced optimization algorithms have recently demonstrated significant success in speeding up the solving process. This work introduces a neural-accelerated ADMM variant that replaces exact subproblem solutions with learned approximations through a parameter-efficient Long Short-Term Memory (LSTM) network. We derive convergence guarantees within the inexact ADMM formalism, establishing that our learning-augmented method maintains primal-dual convergence while satisfying residual thresholds. Extensive experimental results demonstrate that our approach achieves superior solution accuracy compared to existing learning-based methods while delivering significant computational speedups of up to $7\times$, $28\times$, and $22\times$ over Gurobi, SCS, and OSQP, respectively. Furthermore, the proposed method outperforms other learning-to-optimize methods in terms of solution quality. Detailed performance analysis confirms near-perfect compliance with the theoretical assumptions, consequently ensuring algorithm convergence.