Self-Supervised Learning of Iterative Solvers for Constrained Optimization
This addresses the need for high-accuracy, real-time optimization in applications like model predictive control, offering a novel self-supervised approach with theoretical guarantees.
The paper tackles the real-time solution of parametric optimization problems by presenting a learning-based iterative solver that uses a neural network predictor and a learned iterative solver, achieving speedups of up to one order of magnitude compared to IPOPT and orders of magnitude higher accuracy than other learning-based methods.
The real-time solution of parametric optimization problems is critical for applications that demand high accuracy under tight real-time constraints, such as model predictive control. To this end, this work presents a learning-based iterative solver for constrained optimization, comprising a neural network predictor that generates initial primal-dual solution estimates, followed by a learned iterative solver that refines these estimates to reach high accuracy. We introduce a novel loss function based on Karush-Kuhn-Tucker (KKT) optimality conditions, enabling fully self-supervised training without pre-sampled optimizer solutions. Theoretical guarantees ensure that the training loss function attains minima exclusively at KKT points. A convexification procedure enables application to nonconvex problems while preserving these guarantees. Experiments on two nonconvex case studies demonstrate speedups of up to one order of magnitude compared to state-of-the-art solvers such as IPOPT, while achieving orders of magnitude higher accuracy than competing learning-based approaches.