线性策略的规范性学习框架：为二元决策提供可行性保证
Prescriptive Learning of Linear Policies with Feasibility Guarantees for Binary Decision-Making
搞运筹优化的人可以看看这篇：作者不学预测标签，而是训练时直接联合优化线性策略和可行分配，还加了Wasserstein鲁棒约束保证可行。在分布偏移场景下比传统预测式学习省了最多76.5%成本，做电力调度或排班系统的工程师值得跑一下案例复现。
一篇arXiv论文提出面向二元决策问题的规范性学习（prescriptive learning）框架，覆盖能源调度、交通和人力排班等混合整数优化场景。与传统预测式学习从标注数据中复现最优决策不同，该框架在训练阶段联合优化线性决策策略与可行分配，直接把可行替代方案及其运行绩效纳入训练过程。
作者进一步将框架扩展为基于Wasserstein模糊集的分布鲁棒机会约束形式，可在最坏分布下以指定概率保证可行性，并提供鲁棒性与解质量之间的可调权衡。在机组组合（unit commitment）和人员分配两个案例中，分布内测试时鲁棒模型偏保守，但在分布偏移下相对经典预测式学习将未满足需求大幅降低，总成本最多下降76.5%。
对将机器学习用于替代或加速混合整数求解器的团队而言，这项工作指出了预测式方法在反事实信息和可行性保证上的缺口，并给出可直接落地的建模路径。
Prescriptive Learning of Linear Policies with Feasibility Guarantees for Binary Decision-Making
Binary decision-making under uncertainty arises across a wide range of applications, including energy systems scheduling, transportation, and workforce planning. While machine learning has been increasingly applied to accelerate or replace mixed-integer solvers in such settings, existing approaches rely on predictive learning, training models to reproduce optimal decisions from labeled data, which lacks knowledge of counterfactual outcomes and provides no guarantees that the resulting decisions will be feasible. This limitation is further compounded under distributional shift, where policies trained on historical data may produce systematically infeasible decisions. We propose a prescriptive learning framework for binary decision-making that addresses both limitations. Rather than predicting optimal labels, the framework jointly optimizes over linear decision policies and feasible assignments across all training scenarios, allowing feasible alternatives and their operational performance to be considered directly during training. We further extend the framework to a distributionally robust chance-constrained formulation using a Wasserstein ambiguity set, which enforces feasibility with a prescribed probability under the worst-case distribution in the ambiguity set and enables a tunable trade-off between robustness and solution quality. We demonstrate the framework on two case studies, namely a unit commitment problem and a staff allocation problem. Out-of-sample experiments under test distributions that either match or differ from the training distribution show that the robust model is more conservative when the two distributions coincide, while under distributional shift it substantially reduces unmet demand and lowers total cost by up to 76.5% relative to classical predictive learning.
本条情报归属 AITOP「论文」核心追踪栏目。涉及核心实体与技术议题包括：规范性学习、Wasserstein模糊集、混合整数优化、分布鲁棒优化，读者可通过下方标签进入对应专题页查阅历史脉络与关联对比。
信源核验说明：本文原始线索采编自「arXiv cs.LG」（@Farzaneh Pourahmadi, Trine Krogh Boomsma, Pierre Pinson），经 AITOP 多维评分管线结构化提炼。