用神经网络快速求解带约束优化问题，比传统方法快10倍且更准。
Self-Supervised Learning of Iterative Solvers for Constrained Optimization
- 用神经网络预测初始解，再通过学习的迭代过程精修至高精度。
- 在两个非凸案例中，速度比IPOPT快10倍，精度远超其他学习方法。
- 无需真实解监督，靠KKT条件自动训练，适合实时控制等场景。
实时求解参数化优化问题对模型预测控制等需高精度与强时效性的应用至关重要。本文提出一种基于学习的约束优化迭代求解器，包含一个生成初始原对偶解估计的神经网络，随后由学习的迭代求解器精炼该估计以达到高精度。我们引入一种基于Karush-Kuhn-Tucker（KKT）最优性条件的新损失函数，实现完全自监督训练，无需预先求解的优化器结果。理论保证表明，该损失函数仅在KKT点处取得最小值。通过凸化处理，可将方法扩展至非凸问题并保持上述性质。在两个非凸案例上的实验表明，相比主流求解器IPOPT，速度提升达一个数量级，同时精度比现有学习方法高出数个数量级。
原文摘要 · Abstract (English)
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-solved 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.
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