论文标题
部分可观测时空混沌系统的无模型预测
Data-Driven Approximations of Chance Constrained Programs in Nonstationary Environments
论文作者
论文摘要
我们研究偶然限制程序的样本平均近似值（SAA）。 SAA方法通常使用从假定独立的随机样本构建的经验分布构建的经验分布中近似于机会约束，并根据实际分布相同分布。在本文中，我们考虑了此问题的一个非组织变体，其中假定随机样品是从未知且可能是时间变化的分布中独立绘制的。这种非平稳性可能是由许多现实世界中存在的环境条件变化而驱动的。为了说明数据生成过程中潜在的非机构性，我们提出了一种新颖的鲁棒SAA方法，利用了有关数据生成分布的序列与实际机会约束分布之间的Wasserstein距离的信息。作为关键结果，我们获得了确保强大的SAA方法所需的样本量的无分配估计值，这些解决方案将产生可行的解决方案，这些解决方案在实际分布下以高置信度在实际分布下可行。
We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be independent and identically distributed according to the actual distribution. In this paper, we consider a nonstationary variant of this problem, where the random samples are assumed to be independently drawn in a sequential fashion from an unknown and possibly time-varying distribution. This nonstationarity may be driven by changing environmental conditions present in many real-world applications. To account for the potential nonstationarity in the data generation process, we propose a novel robust SAA method exploiting information about the Wasserstein distance between the sequence of data-generating distributions and the actual chance constraint distribution. As a key result, we obtain distribution-free estimates of the sample size required to ensure that the robust SAA method will yield solutions that are feasible for the chance constraint under the actual distribution with high confidence.
