AI 中文总结
本文提出集成学习与鲁棒优化（ILRO）框架，通过凸替代RSPO+等方法实现鲁棒性与学习-决策对齐，在交通和投资组合问题的实验中展现出决策质量优势，尤其在样本有限等场景中效果更显著。
AI 中文摘要
许多运营决策需要求解线性规划，其成本向量在决策时未知，必须从上下文信息中预测。由于预测与决策仅存在弱对齐关系，新兴的集成学习与优化（ILO）范式通过下游问题训练预测器，依据预测结果所产生的决策来评判预测质量。然而预测不可避免地存在不精确性，因此决策阶段常需引入鲁棒性。为解决该问题，我们提出集成学习与鲁棒优化（ILRO）框架，其中鲁棒决策问题既用于定义训练问题（称为RSPO损失问题），又用于生成部署决策。该框架同时实现了鲁棒性与学习-决策对齐。为应对其计算挑战，我们开发了凸替代RSPO+，并刻画了其Fisher一致性的成立条件。此外，RSPO损失具有信息丰富的梯度，使我们能开发一阶计算方法。我们还推导了RSPO与RSPO+预测器的有限样本超额风险界。在交通与投资组合问题上的数值实验表明，与多个基准相比，所提框架在决策质量上具有优势，且在样本有限、决策维度高、模型误设的场景中，该优势更为显著。
英文摘要
Many operational decisions require solving a linear program whose cost vector is unknown at decision time and must be predicted from contextual information. Because prediction and decision are only weakly aligned, the emerging integrated learning and optimization (ILO) paradigm trains the predictor through the downstream problem, judging a prediction by the decision it induces. However, predictions are inevitably imprecise, so robustness often enters the decision stage. To address this issue, we propose an integrated learning and robust optimization (ILRO) framework, where a robust decision problem is used both to define the training problem (termed the RSPO loss problem), and to produce the deployed decision. Thus, this framework simultaneously achieves both robustness and learning-decision alignment. To tackle its computational challenges, we develop a convex surrogate, RSPO+, and characterize when it is Fisher consistent. Moreover, the RSPO loss possesses informative gradients, allowing us to develop first-order computational methods. We also derive finite-sample excess risk bounds for both RSPO and RSPO+ predictors. Numerical experiments on transportation and portfolio problems, in comparison with multiple benchmarks, show the advantage in decision quality of the proposed framework. The gain is more pronounced for scenarios with limited samples, high-dimensional decisions, and model misspecification.
