This tutorial survey provides an overview of recent non-asymptotic advances in statistical learning theory as relevant to control and system identification. While there has been substantial progress across all areas of control, the theory is most well-developed when it comes to linear system identification and learning for the linear quadratic regulator, which are the focus of this manuscript. From a theoretical perspective, much of the labor underlying these advances has been in adapting tools from modern high-dimensional statistics and learning theory. While highly relevant to control theorists interested in integrating tools from machine learning, the foundational material has not always been easily accessible. To remedy this, we provide a self-contained presentation of the relevant material, outlining all the key ideas and the technical machinery that underpin recent results. We also present a number of open problems and future directions.
翻译:这份辅导性调查概述了统计学理论中与控制和系统识别有关的近期非被动性进展,尽管在所有控制领域都取得了实质性进展,但理论在线性系统识别和对线性二次调节器的学习方面最为发达,而线性二次调节器正是这一手稿的重点。从理论的角度来看,这些进步背后的大部分工作是从现代高维统计和学习理论中改编工具。虽然这些进步对于控制有兴趣从机器学习中整合工具的理论家非常重要,但基础材料并非总能轻易获得。为了纠正这一点,我们提供了相关材料的自成一体的介绍,概述了作为最近成果基础的所有关键想法和技术机制。我们还提出了一些公开的问题和今后的方向。