让预测参数同时保证可行性和决策质量,提升优化可靠性。
Feasibility-Aware Decision-Focused Learning for Predicting Parameters in the Constraints
- 设计双损失函数,分别惩罚不可行解和次优解
- 通过调节权重平衡可行性与决策质量,实验验证有效
- 适用于任意约束优化问题,不依赖线性假设
当约束优化问题(COP)中的部分参数不确定时,会形成预测-然后-优化(PtO)问题,包含从上下文信息预测未知参数,再用预测值进行优化两个阶段。决策聚焦学习(DFL)通过训练机器学习模型来优化预测参数所带来决策的质量。当预测参数出现在约束中时,可能导致不可行解。因此需同时兼顾可行性与决策质量。本文提出一种通用COP的决策聚焦学习框架,无需假设优化问题为线性规划(LP)或整数线性规划(ILP)。基于最大似然估计(MLE),推导出两种新损失函数:第一种惩罚导致不可行解的预测参数;第二种惩罚使真实最优解不可行的预测参数。引入一个可调参数,对两损失加权平均,使决策者可灵活控制可行性与子最优性的权衡。实验表明,调整该参数可实现对两者优先级的调控,在多个COP实例中均优于现有基线方法,无论以可行性还是决策质量为目标。
原文摘要 · Abstract (English)
When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the subsequent optimization using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.
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