用成本敏感回归提升决策优化训练效率,省去反复求解。
Scalable Decision-Focused Learning through Cost-Sensitive Regression

- 将优化学习重构为多输出成本敏感回归问题
- 仅需每样本0或1次求解,训练速度大幅提升
- 适合大规模不确定参数优化场景,可扩展至新规模
许多现实中的组合优化问题涉及不确定参数,可通过上下文特征和历史数据进行预测。传统‘先预测后优化’方法已转向端到端训练,直接最小化下游任务成本而非预测误差。然而,现有决策聚焦学习(DFL)方法在训练中频繁求解优化问题,计算开销大,难以扩展。本文将学习问题重新建模为成本敏感的多输出回归:因优化问题含多个不确定参数而为多输出,以任务成本为真实目标而具成本敏感性。技术贡献在于形式化三类损失组件:成本无关归一化、决策感知的过/低估不对称惩罚,以及模拟真实任务损失的实例级成本。这些组件只需每样本0或1次求解,训练期间无需额外求解。实验表明,该组合在下游任务质量上达到当前最优水平,同时显著提升效率,首次实现对大规模问题的决策聚焦学习。
原文摘要 · Abstract (English)
Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.
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