发表机构
Auburn University; University of Alabama（奥本大学; 阿拉巴马大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对线性优化中决策聚焦学习的非光滑问题，证明平均后曲率局部二次，给出闭合形式及可计算近似，并应用于场景生成，实验显示30.8%的遗憾改进。
AI 中文摘要
决策聚焦学习在线性优化中因优化器的不连续性而变得复杂，其中小的成本误差可能使决策保持不变或将其移至另一个顶点。我们表明，这种非光滑的点态行为在数据分布上取平均后变为局部二次的，并推导出闭合形式的曲率，具体为一个支撑在法向扇区壁上的矩阵值测度。该测度仅依赖于可行集，数据分布仅作为权重进入。然后，我们为这种曲率提供了一种可处理的近似，仅需一次投影到可行集即可计算。我们证明该近似弱收敛于真实的总体曲率。我们提供了我们发现的一个应用，即用于期望成本线性优化的决策感知场景生成方法。我们的实验测试了二次和弱收敛定律，并显示在电池套利上比均匀分配有30.8%的遗憾改进。
英文摘要
Decision-focused learning for linear optimization is complicated by the discontinuity of the optimizer, where small cost errors may leave the decision unchanged or move it to a different vertex. We show that this non-smooth pointwise behavior becomes locally quadratic after averaging over the data distribution, and we derive the curvature in closed form, specifically, a matrix-valued measure supported on the walls of the normal fan. This measure depends only on the feasible set, with the data distribution entering only as a weight. We then offer a tractable approximation for this curvature, computable with just one projection to the feasible set. We prove that the approximation weakly converges to the true population curvature. We offer one application of our findings, a decision-aware scenario generation method for expected-cost linear optimization. Our experiments test the quadratic and weak convergence laws and show a 30.8% regret improvement over uniform allocation on battery arbitrage.
Comments4 pages main body plus appendix, 3 figures. Accepted to the NeurIPS 2026 Workshop on MLxOR
