Learning Over-Relaxation Policies for ADMM with Convergence Guarantees

2026-04-29 · Source: Takara TLDR - Daily AI Papers · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, medium

Summary

A new method for optimizing the Alternating Direction Method of Multipliers (ADMM) has been developed, focusing on learning online updates for the relaxation parameter. This approach, detailed in a paper from April 29, 2026, by Luca Furieri, Junan Lin, and Paul J. Goulart, aims to enhance ADMM's practical performance in structured convex optimization, particularly in settings like Model Predictive Control (MPC) where similar problems are solved repeatedly. The key advantage is that adapting the relaxation parameter avoids the computationally expensive matrix refactorizations required for penalty parameter updates in OSQP-like architectures. The authors provide convergence guarantees for ADMM with time-varying parameters and demonstrate that their learned policies improve both iteration count and wall-clock time on benchmark quadratic programs compared to baseline OSQP.

Key takeaway

For research scientists developing or deploying optimization algorithms in dynamic environments like Model Predictive Control, you should investigate integrating learned relaxation parameter policies into your ADMM implementations. This approach offers significant computational benefits by avoiding matrix refactorizations, potentially leading to faster convergence and reduced wall-clock times without sacrificing theoretical convergence guarantees.

Key insights

Learning ADMM relaxation parameters online improves performance without costly matrix refactorizations.

Principles

• Time-varying ADMM parameters can maintain convergence.
• Relaxation parameter updates are computationally efficient.

Method

The method involves learning online updates for the ADMM relaxation parameter, establishing convergence guarantees for time-varying parameters, and applying these policies to improve performance on problem classes.

In practice

• Apply to Model Predictive Control (MPC).
• Integrate into OSQP-like optimization architectures.

Topics

• ADMM
• Over-Relaxation Policies
• Convex Optimization
• Model Predictive Control
• Convergence Guarantees

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Robotics Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Takara TLDR - Daily AI Papers.