学习用于决策聚焦的分布鲁棒优化的预测模糊集
Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization
AI总结：
研究针对预测后优化系统的不足，提出学习预测模糊集方法，通过深度上下文模型输出相关参数定义模糊集，经特定训练使半径自适应，用于分布鲁棒投资组合优化，效果优于多种基线，能减少保守性并提高适应性。
AI中文摘要：
预测后优化系统通常将不确定性压缩为点预测，然后如同预测可靠般解决下游优化问题。分布鲁棒优化（DRO）能防范错误设定，但模糊集常以历史样本为中心且半径固定。我们提出学习预测模糊集（LPAS）：深度上下文模型输出有限名义情景分布、状态依赖的 Wasserstein 半径及可选的各向异性基础度量。这些输出定义上下文模糊集以馈入 DRO 决策层。半径通过条件分位数校准、大小正则化和下游决策损失组合训练，使鲁棒性具有适应性而非全局固定。我们推导决策层使用的有限对偶形式，给出分阶段训练算法，并在 2018 - 2026 年标准普尔 500 指数的 20 个成分股的分布鲁棒投资组合优化中评估该方法。所提方法大幅优于等权重、预测后优化和历史 Wasserstein DRO 基线，实现年化收益率 26.28%，夏普比率 1.30，最终财富 1.61，且下尾损失低于深度固定半径 DRO 基线，同时平均半径更小。结果表明，学习到的模糊半径能在减少不必要保守性并提高状态适应性的同时，恢复大部分强固定半径 DRO 的性能。
英文摘要：
Predict-then-optimize systems usually compress uncertainty into a point forecast and then solve a downstream optimization problem as if the forecast were reliable. Distributionally robust optimization (DRO) offers protection against misspecification, but the ambiguity set is often centered at historical samples and uses a fixed radius. We propose \emph{learned predictive ambiguity sets} (LPAS): a deep contextual model outputs a finite nominal scenario distribution, a state-dependent Wasserstein radius, and optionally an anisotropic ground metric. These outputs define a contextual ambiguity set that feeds a DRO decision layer. The radius is trained by a combination of conditional quantile calibration, size regularization, and downstream decision loss, so that robustness is adaptive rather than globally fixed. We derive the finite dual form used by the decision layer, present a staged training algorithm, and evaluate the method on distributionally robust portfolio optimization with 20 S&P 500 constituents from 2018--2026. The proposed method substantially improves over equal-weight, predict-then-optimize, and historical Wasserstein DRO baselines, achieving 26.28% annualized return, Sharpe ratio 1.30, final wealth 1.61, and lower tail loss than a deep fixed-radius DRO baseline while using a smaller average radius. The results show that learned ambiguity radii can recover most of the performance of strong fixed-radius DRO while reducing unnecessary conservatism and improving regime adaptivity.
