Statistical Learning Theory for Control: A Finite Sample Perspective

TL;DR

This survey reviews recent non-asymptotic statistical learning theory advances applied to control, focusing on linear systems and LQR, highlighting theoretical tools, key ideas, and open problems for control and system identification.

Contribution

It provides a self-contained overview of modern high-dimensional statistical tools applied to control, emphasizing linear system identification and LQR, with accessible explanations and future research directions.

Findings

Advances in non-asymptotic learning theory for control

Application of high-dimensional statistics to linear systems

Open problems and future research directions

Abstract

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.