用置信预测收紧优化解的差距，提升决策可靠性
Tightening optimality gap with confidence through conformal prediction
- 基于选择性推断处理边界值的异方差问题
- 在相同置信水平下，预测区间更紧致，效率更高
- 适合需要精准评估解优度的工业优化场景
决策者常使用约束优化技术规划与运行复杂系统，如全球供应链或电网。在此背景下，从业者需评估计算解与最优解的接近程度，以决定当前解是否足够或是否需额外计算。常用方法是利用优化求解器返回的对偶界评估解的质量。尽管这些对偶界具有认证保证，但通常过于宽松，难以提供实际参考价值。本文提出一种新的置信预测框架，用于收紧松散的原始解和对偶界。该方法通过选择性推断处理这些界中常见的异方差现象，并进一步利用其固有的认证有效性，生成更紧致、更具信息量的预测区间。最后，在大规模工业问题上的数值实验表明，该方法可在相同覆盖水平下比基线方法更高效地提供结果。
原文摘要 · Abstract (English)
Decision makers routinely use constrained optimization technology to plan and operate complex systems like global supply chains or power grids. In this context, practitioners must assess how close a computed solution is to optimality in order to make operational decisions, such as whether the current solution is sufficient or whether additional computation is warranted. A common practice is to evaluate solution quality using dual bounds returned by optimization solvers. While these dual bounds come with certified guarantees, they are often too loose to be practically informative. To this end, this paper introduces a novel conformal prediction framework for tightening loose primal and dual bounds. The proposed method addresses the heteroskedasticity commonly observed in these bounds via selective inference, and further exploits their inherent certified validity to produce tighter, more informative prediction intervals. Finally, numerical experiments on large-scale industrial problems suggest that the proposed approach can provide the same coverage level more efficiently than baseline methods.
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