To scale the solution of optimization and simulation problems, prior work has explored machine-learning surrogates that inexpensively map problem parameters to corresponding solutions. Commonly used approaches, including supervised and self-supervised learning with either soft or hard feasibility enforcement, face inherent challenges such as reliance on expensive, high-quality labels or difficult optimization landscapes. To address their trade-offs, we propose a novel framework that first collects "cheap" imperfect labels, then performs supervised pretraining, and finally refines the model through self-supervised learning to improve overall performance. Our theoretical analysis and merit-based criterion show that labeled data need only place the model within a basin of attraction, confirming that only modest numbers of inexact labels and training epochs are required. We empirically validate our simple three-stage strategy across challenging domains, including nonconvex constrained optimization, power-grid operation, and stiff dynamical systems, and show that it yields faster convergence; improved accuracy, feasibility, and optimality; and up to 59x reductions in total offline cost.

翻译：为扩展优化与仿真问题的求解规模，先前研究已探索使用机器学习代理模型，将问题参数低成本映射至对应解。常用方法（包括采用软约束或硬约束的监督学习与自监督学习）面临固有挑战，如依赖昂贵的高质量标签或复杂的优化地形。为权衡这些因素，我们提出一种新颖框架：首先收集“廉价”的不完美标签，随后进行监督预训练，最终通过自监督学习精炼模型以提升整体性能。理论分析与基于性能的准则表明，标注数据仅需将模型置于吸引域内，这证实仅需少量不精确标签和训练周期即可实现目标。我们在非凸约束优化、电网运行和刚性动力系统等挑战性领域中实证验证了这一简单的三阶段策略，结果表明该方法能实现更快的收敛速度，提升准确性、可行性与最优性，并将离线总成本降低高达59倍。