论文标题
部分可观测时空混沌系统的无模型预测
Distributionally Robust Decision Making Leveraging Conditional Distributions
论文作者
论文摘要
分布强劲的优化（DRO）是在不确定性下进行决策的强大工具。由于其能够利用现有数据的能力，因此特别有吸引力。但是，许多实际问题都要求使用一些辅助信息进行决策，而在条件分布的背景下DRO并不简单。我们提出了一种有条件的内核分布在鲁棒优化的方法（CKDRO）方法，该方法可以通过内核DRO进行有条件分布的强大决策以及在再现核心Hilbert Space（RKHS）中的条件平均操作员。特别是，我们考虑了未知变量与可观察变量x之间存在相关性的问题。给定两个变量的过去数据和一个查询的辅助变量，CKDRO代表条件分布p（y | x）作为RKHS空间中的条件平均操作员，并量化了RKHS中的歧义性歧义，这取决于数据集的大小以及Query点。为了证明RKH的使用是合理的，我们证明了RKHS中定义的歧义集可以被视为与Wasserstein Metric相似的度量标准下的球。然后通过有限的尺寸凸面程序进行双重化并求解DRO。提出的CKDRO方法应用于一代调度问题，并表明CKDRO的结果优于质量和鲁棒性的常见基准。
Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distribution is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.
