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.

翻译：许多现实世界的组合优化问题涉及不确定参数，这些参数可以根据上下文特征和历史数据进行预测。这类“预测-优化”或“上下文优化”问题已引起广泛关注：端到端训练方法现在可以最小化下游任务成本，而非预测误差。然而，尽管这些决策聚焦学习（DFL）方法有效，它们通常在训练期间依赖反复求解底层组合优化问题，导致计算成本高昂且难以扩展。我们将学习问题重新框架化为一个代价敏感的多输出回归问题：多输出源于组合问题包含多个不确定参数，而代价敏感则因下游任务成本才是真正的目标。我们的技术贡献在于形式化了从这一重新框架化中得出的多个损失函数组件：代价不敏感归一化、对过高和过低预测的决策感知不对称惩罚，以及局部模拟真实下游任务损失的实例级成本。这些组件每个训练数据实例仅需零次或一次求解，同时训练期间无需进一步求解。实验表明，这些损失组件的组合在达到与现有技术相当的下游任务质量的同时，效率显著提升，从而能够扩展到此前DFL方法未能应对的问题规模。