Paper Overview
Field: Machine Learning Authors: Junan Lin, Paul J. Goulart, Luca Furieri Published: 2025-04-30 arXiv: 2504.20813
English Translation
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 performance on problem classes of interest. This choice is computationally attractive in 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 programming problems that the resulting learned policies improve both iteration counts and wall-clock times compared to baseline OSQP.
Key Points
- Learns online update policies for the relaxation parameter of ADMM, rather than the penalty parameter.
- Targeted at repeated solving of related problems (e.g., MPC) with fixed structure and varying parameters.
- Relaxation updates avoid the costly matrix refactorizations that penalty updates require in OSQP-like solvers.
- Provides convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions.
- Empirical results on benchmark QPs show improvements in both iterations and wall-clock time over baseline OSQP.