AI 中文总结
研究智能预测然后优化方法的稳健变体，通过智能预测然后稳健优化损失集成稳健优化原则，建立凸代理防范特征扰动，理论证明其有效性及优势，数值实验验证该稳健框架性能优于标准方法。
AI 中文摘要
在本文中，我们提出并研究了智能预测然后优化方法的一种稳健变体，该变体考虑了协变量特征空间中由于干扰导致的预测偏移。传统的集成学习与优化模型假设辅助信息能完美揭示，但经验数据驱动的特征在决策时经常被破坏或有噪声，导致操作策略脆弱。为弥合这一差距，我们通过智能预测然后稳健优化损失将稳健优化原则直接集成到预测 - 规定管道中，并建立了一个易于计算的凸代理，旨在防范最坏情况的特征扰动。在理论方面，我们通过证明其近似误差概率根据次高斯集中分布呈指数衰减来形式化该代理的结构有效性。此外，我们确定在温和假设下，该代理以高概率是费舍尔一致的。我们还证明了我们的框架优于标准智能预测然后优化的必要条件，并且即使标准方法配备正则化上游预测时也能保持其优越性。数值实验验证了我们的稳健框架在样本外和训练稳定性方面都始终比标准方法有显著的性能提升。
英文摘要
In this paper, we propose and study a robust variant of the smart predict-then-optimize approach that accounts for prediction shifts due to disturbance in the covariate feature space. While traditional integrated-learning-and-optimization models assume that side information is perfectly revealed, empirical data-driven features are frequently corrupted or noisy at the time of decision-making, leading to fragile operational policies. To bridge this gap, we integrate principles of robust optimization directly into the predictive-prescriptive pipeline via a smart predict-then-robustly optimize loss and establish a computationally tractable convex surrogate, designed to hedge against worst-case feature perturbations. On the theoretical front, we formalize the structural validity of this surrogate by proving its approximation error probability decays exponentially according to a sub-Gaussian concentration profile. Furthermore, we establish that under mild assumptions, the surrogate is Fisher consistent with high probability. We also prove necessary conditions under which our framework outperforms standard smart predict-then-optimize and maintain its superiority even when the standard method is equipped with regularized upstream predictions. Numerical experiments validate that our robust framework consistently yields significant performance improvements over standard methods, both in out-of-sample terms and in training stability.
