论文标题
分布强劲的随机程序，并基于饰带的侧面信息 - 扩展版本
Distributionally robust stochastic programs with side information based on trimmings -- Extended version
论文作者
论文摘要
我们考虑以某些协变量信息为条件的随机程序，在这种情况下，对不确定参数和协变量之间可能关系的唯一知识将减少为其关节分布的有限数据样本。通过利用概率度量的修剪概念与部分质量运输问题之间的密切联系，我们构建了一个数据驱动的分布在强大的优化框架（DRO）框架，以对冲在从有限的关节数据中推断有条件信息的过程中针对内在误差的决定。我们表明，我们的方法在计算上与标准（没有侧面信息）的基于Wasserstein-metric的DRO一样可拖动，并享有性能保证。此外，我们的DRO框架可以方便地用于解决受污染的样本下的数据驱动决策问题，并且自然会生成某些本地非参数预测方法的分布强大的版本，例如Nadaraya-Watson kernel kernel kernel kernel Recription和$ k $ $ k $ $ $ neart的邻居，这些邻居经常在条件上使用。最后，使用单项新闻顾问问题和带有侧面信息的投资组合分配问题来说明理论结果。
We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint distribution. By exploiting the close link between the notion of trimmings of a probability measure and the partial mass transportation problem, we construct a data-driven Distributionally Robust Optimization (DRO) framework to hedge the decision against the intrinsic error in the process of inferring conditional information from limited joint data. We show that our approach is computationally as tractable as the standard (without side information) Wasserstein-metric-based DRO and enjoys performance guarantees. Furthermore, our DRO framework can be conveniently used to address data-driven decision-making problems under contaminated samples and naturally produces distributionally robust versions of some local nonparametric predictive methods, such as Nadaraya-Watson kernel regression and $K$-nearest neighbors, which are often used in the context of conditional stochastic optimization. Finally, the theoretical results are illustrated using a single-item newsvendor problem and a portfolio allocation problem with side information.
