🤖 AI Summary
This work proposes an online learning strategy for accelerating the convergence of the Alternating Direction Method of Multipliers (ADMM) when solving structured convex optimization problems—such as time-varying quadratic programs arising in model predictive control—by dynamically tuning its relaxation parameter. The approach targets scenarios where the problem structure remains fixed but parameters change over time, thereby circumventing the need for costly matrix refactorizations typically required in conventional penalty parameter adjustment. For the first time, convergence guarantees are established for ADMM with time-varying penalty and relaxation parameters. By integrating ideas from reinforcement learning into parameter scheduling, the method achieves substantial improvements in solution efficiency while maintaining low computational overhead. Implemented within the OSQP framework, the proposed strategy significantly reduces both iteration counts and actual solve times on standard quadratic programming benchmarks.
📝 Abstract
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 programs that the resulting learned policies improve both iteration count and wall-clock time over baseline OSQP.