预测后优化还是生成后优化：学术研究对比两种情境决策路径
Contextual Decision Making: Predictive or Generative
搞运筹或决策优化的朋友可以看看，这篇把 PtO 和 GtO 两条路线的 regret 边界和凸性权衡讲清楚了，选方法前能少踩坑。
arXiv 论文 2610.32584 对比了情境决策中的两种方法：predict-then-optimize（PtO）学习条件期望目标，generate-then-optimize（GtO）学习条件不确定性并用生成场景做优化。研究通过 regret 边界分析学习目标的选择如何影响统计精度与优化可行性，发现 PtO 目标更窄，但 GtO 可借助平滑性弥补额外维度负担。论文还指出优化层面的权衡：PtO 类非负权重方法存在下界，限制了平滑性带来的收益，而引入带符号权重的灵活方法会失去保持凸性的保证。合成实验与真实案例展示了这些权衡如何随数据量和问题结构变化，结论是不存在普适赢家。
Contextual Decision Making: Predictive or Generative
Contextual decision making uses observed covariates to guide decisions under uncertainty. Two natural approaches are predict-then-optimize (PtO), which learns the conditional expected objective, and generate-then-optimize (GtO), which learns conditional uncertainty and optimizes using generated scenarios. We study when each approach is preferable by examining how the choice of learning target affects statistical accuracy and optimization tractability. Although PtO learns a narrower target, our regret bounds show how differences in smoothness can offset GtO's additional dimensional burden. Exploiting smoothness also raises an optimization tradeoff: within the class of nonnegative-weight PtO methods studied, a lower bound limits the gains from additional smoothness, while more flexible methods may introduce signed weights and lose the guarantee of preserving convexity. GtO preserves scenario-wise convexity, but requires learning a richer object and generating scenarios for optimization. Synthetic experiments and a real case study illustrate how these tradeoffs vary with data availability and problem structure. Together with the scope for reusing a model across tasks, our findings provide practical guidance for choosing between the approaches without identifying a universal winner.