Self-Supervised Learning of Iterative Solvers for Constrained Optimization

TL;DR

This paper introduces a self-supervised learning framework for iterative constrained optimization solvers that significantly accelerates solution times while maintaining high accuracy, applicable to real-time control tasks.

Contribution

It proposes a neural network-based predictor and iterative solver trained with a novel KKT-based loss, with theoretical guarantees and a convexification method for nonconvex problems.

Findings

Achieves up to 10x speedup over IPOPT.

Attains higher accuracy than existing learning-based methods.

Validates approach on nonconvex case studies.

Abstract

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.