# Learning Over-Relaxation Policies for ADMM with Convergence Guarantees

arXiv: https://arxiv.org/abs/2604.26932 · HTML: https://mlsanity.com/paper/2604.26932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 21 references that are in the map.
- First posted on arXiv 29 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Accelerating Quadratic Optimization with Reinforcement Learning](https://mlsanity.com/paper/2107.10847/) (2021)
- [A General Analysis of the Convergence of ADMM](https://mlsanity.com/paper/1502.02009/) (2015)
- [Adaptive ADMM with Spectral Penalty Parameter Selection](https://mlsanity.com/paper/1605.07246/) (2016)
- [Learning to optimize with convergence guarantees using nonlinear system theory](https://mlsanity.com/paper/2403.09389/) (2024)
- [Learning Algorithm Hyperparameters for Fast Parametric Convex Optimization](https://mlsanity.com/paper/2411.15717/) (2024)
- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms](https://mlsanity.com/paper/2508.00775/) (2025)
- [Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation](https://mlsanity.com/paper/1704.02712/) (2017)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [The Degenerate Variable Metric Proximal Point Algorithm and Adaptive Stepsizes for Primal-Dual Douglas-Rachford](https://mlsanity.com/paper/2302.13128/) (2023)
- [SuperADMM: Solving Quadratic Programs Faster with Dynamic Weighting ADMM](https://mlsanity.com/paper/2506.11608/) (2025)

## Abstract (arXiv)

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such as Model Predictive Control (MPC), where one repeatedly solves related optimization problems with fixed structure and changing parameter values, we propose learning online updates of the relaxation parameter to improve average performance on problem classes of interest, while guaranteeing that asymptotic convergence is not compromised for the worst-case realization of such problems. This choice is computationally attractive in the Operator Splitting Quadratic Program (OSQP)-like architectures, since adapting relaxation does not trigger the matrix refactorizations associated with penalty updates. We establish convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions, and show on benchmark quadratic programs that the resulting learned policies improve both iteration count and wall-clock time on average over baseline OSQP.