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：本教程综述概述了统计学习理论中近期与控制和系统辨识相关的非渐进性进展。尽管控制领域各方面均取得显著进步，但线性系统辨识及线性二次型调节器的学习理论最为成熟，这也是本文的重点。从理论角度看，这些进展背后的核心工作多源于对现代高维统计学与学习理论工具的适配。虽然这些内容对希望整合机器学习工具的控制理论研究者至关重要，但其基础材料往往不易获取。为解决这一问题，我们提供了相关材料的自包含式阐述，系统梳理了支撑最新成果的所有核心思想与技术机制，并提出了若干开放性问题与未来研究方向。