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Learning to Control...
Learning to Control Linear Systems can be Hard
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- Tsiamis, Anastasios (författare)
- Automatic Control Laboratory, ETH Zurich, Switzerland
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- Ziemann, Ingvar (författare)
- KTH,Reglerteknik
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- Morari, Manfred (författare)
- Department of Electrical and Systems Engineering, University of Pennsylvania, United States
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visa fler...
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- Matni, Nikolai (författare)
- Department of Electrical and Systems Engineering, University of Pennsylvania, United States
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- Pappas, George J. (författare)
- Department of Electrical and Systems Engineering, University of Pennsylvania, United States
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visa färre...
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(creator_code:org_t)
- ML Research Press, 2022
- 2022
- Engelska.
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Ingår i: Proceedings of 35th Conference on Learning Theory, COLT 2022. - : ML Research Press. ; , s. 3820-3857
- Relaterad länk:
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https://urn.kb.se/re...
Abstract
Ämnesord
Stäng
- In this paper, we study the statistical difficulty of learning to control linear systems. We focus on two standard benchmarks, the sample complexity of stabilization, and the regret of the online learning of the Linear Quadratic Regulator (LQR). Prior results state that the statistical difficulty for both benchmarks scales polynomially with the system state dimension up to system-theoretic quantities. However, this does not reveal the whole picture. By utilizing minimax lower bounds for both benchmarks, we prove that there exist nontrivial classes of systems for which learning complexity scales dramatically, i.e. exponentially, with the system dimension. This situation arises in the case of underactuated systems, i.e. systems with fewer inputs than states. Such systems are structurally difficult to control and their system theoretic quantities can scale exponentially with the system dimension dominating learning complexity. Under some additional structural assumptions (bounding systems away from uncontrollability), we provide qualitatively matching upper bounds. We prove that learning complexity can be at most exponential with the controllability index of the system, that is the degree of underactuation.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Publikations- och innehållstyp
- ref (ämneskategori)
- kon (ämneskategori)