Statistical Learning Theory for Control: A Finite-Sample Perspective

Learning algorithms have become an integral component to modern engineering solutions. Examples range from self-driving cars and recommender systems to finance and even critical infrastructure, many of which are typically under the purview of control theory. While these algorithms have already shown...

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Bibliographic Details
Published in:IEEE control systems 2023-12, Vol.43 (6), p.67-97
Main Authors: Tsiamis, Anastasios, Ziemann, Ingvar, Matni, Nikolai, Pappas, George J.
Format: Magazinearticle
Language:English
Subjects:
Algorithm design and theory
Algorithms
Autonomous cars
Control theory
Critical infrastructure
Dynamical systems
Failure modes
Heuristic algorithms
Learning
Learning systems
Learning theory
Machine learning
Machine learning algorithms
Recommender systems
Safety
State-of-the-art reviews
Statistical analysis
Surveys
System identification
Systems theory
Tutorials
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Summary:Learning algorithms have become an integral component to modern engineering solutions. Examples range from self-driving cars and recommender systems to finance and even critical infrastructure, many of which are typically under the purview of control theory. While these algorithms have already shown tremendous promise in certain applications [1] , there are considerable challenges, in particular, with respect to guaranteeing safety and gauging fundamental limits of operation. Thus, as we integrate tools from machine learning into our systems, we also require an integrated theoretical understanding of how they operate in the presence of dynamic and system-theoretic phenomena. Over the past few years, intense efforts toward this goal-an integrated theoretical understanding of learning, dynamics, and control-have been made. While much work remains to be done, a relatively clear and complete picture has begun to emerge for (fully observed) linear dynamical systems. These systems already allow for reasoning about concrete failure modes, thus helping to indicate a path forward. Moreover, while simple at a glance, these systems can be challenging to analyze. Recently, a host of methods from learning theory and high-dimensional statistics, not typically in the control-theoretic toolbox, have been introduced to our community. This tutorial survey serves as an introduction to these results for learning in the context of unknown linear dynamical systems (see "Summary"). We review the current state of the art and emphasize which tools are needed to arrive at these results. Our focus is on characterizing the sample efficiency and fundamental limits of learning algorithms. Along the way, we also delineate a number of open problems. More concretely, this article is structured as follows. We begin by revisiting recent advances in the finite-sample analysis of system identification. Next, we discuss how these finite-sample bounds can be used downstream to give guaranteed performance for learning-based offline control. The final technical section discusses the more challenging online control setting. Finally, in light of the material discussed, we outline a number of future directions.
ISSN:1066-033X
1941-000X
1941-000X
DOI:10.1109/MCS.2023.3310345