🤖 AI Summary
For real-time parametric optimization problems (e.g., model predictive control), this paper proposes an end-to-end self-supervised neural iterative solver: a neural network first generates high-quality initial points, which are then refined by a differentiable primal-dual iterative module. The key contributions are twofold: (i) the design of the first KKT-based, label-free loss function, whose global minima are theoretically guaranteed to coincide exactly with KKT points; and (ii) a local convexification approximation strategy for non-convex problems, extending convergence guarantees to non-convex settings. The method requires no ground-truth labels and enables purely self-supervised training. Evaluated on two canonical non-convex benchmark tasks, it achieves a 10× speedup over IPOPT while attaining solution accuracy orders of magnitude higher than existing learning-based approaches.
📝 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.