针对带不确定约束的上下文线性优化，提出更鲁棒的损失函数与训练策略。
Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints
- 设计了考虑约束不确定性的智能损失函数SPO-RC+，兼顾可行性与预测误差。
- 在背包和合金生产问题上验证，该方法显著提升决策鲁棒性，性能优于基线。
- 适合需处理预测不确定性约束的实际优化场景，如供应链、生产调度。
我们研究了上下文随机线性优化（CSLO）的一个扩展，其中不等式约束依赖于由机器学习模型预测的不确定参数。为应对约束不确定性，采用基于容错预测的上下文不确定性集。给定一种上下文不确定性集构造方法，我们提出“预测后优化-鲁棒约束”（SPO-RC）损失，这是一种对预测目标参数决策误差敏感的可行性感知损失。我们还引入一个凸替代损失SPO-RC+，并证明其与SPO-RC的Fisher一致性。为提升性能，我们在真实约束参数位于不确定性集内的截断数据集上训练，并通过重要性重加权技术校正样本选择偏差。在分数背包和合金生产问题实例上的实验表明，SPO-RC+能有效处理约束不确定性，且结合截断与重要性重加权可进一步提升性能。
原文摘要 · Abstract (English)
We study an extension of contextual stochastic linear optimization (CSLO) that, in contrast to most of the existing literature, involves inequality constraints that depend on uncertain parameters predicted by a machine learning model. To handle the constraint uncertainty, we use contextual uncertainty sets constructed via methods like conformal prediction. Given a contextual uncertainty set method, we introduce the "Smart Predict-then-Optimize with Robust Constraints" (SPO-RC) loss, a feasibility-sensitive adaptation of the SPO loss that measures decision error of predicted objective parameters. We also introduce a convex surrogate, SPO-RC+, and prove Fisher consistency with SPO-RC. To enhance performance, we train on truncated datasets where true constraint parameters lie within the uncertainty sets, and we correct the induced sample selection bias using importance reweighting techniques. Through experiments on fractional knapsack and alloy production problem instances, we demonstrate that SPO-RC+ effectively handles uncertainty in constraints and that combining truncation with importance reweighting can further improve performance.
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