论文标题
基于残差的分布在协变信息上优化可靠的优化
Residuals-based distributionally robust optimization with covariate information
论文作者
论文摘要
我们考虑了将机器学习预测模型集成到分布强劲优化（DRO）之内的数据驱动方法，但对于不确定参数和协变量的关节观察有限。我们的框架很灵活，因为它可以容纳各种回归设置和DRO歧义集。我们研究了使用Wasserstein获得的溶液的渐近和有限样品特性，在我们的DRO公式中采用了样本强大的优化以及基于Phi-Divergence的歧义集，并探索了这些模棱两可的方法的交叉验证方法。通过数值实验，我们验证了我们的理论结果，研究我们对歧义集的方法的有效性，并在有限的数据制度中说明了我们的DRO公式的好处，即使预测模型被误指出。
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.
