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Date
2024-01-19Type
- Conference Paper
ETH Bibliography
yes
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Abstract
We present a local minimax lower bound on the excess cost of designing a linear-quadratic controller from offline data. The bound is valid for any offline exploration policy that consists of a stabilizing controller and an energy bounded exploratory input. The derivation leverages a relaxation of the minimax estimation problem to Bayesian estimation, and an application of van Trees inequality. We show that the bound aligns with system-theoretic intuition. In particular, we demonstrate that the lower bound increases when the optimal control objective value increases. We also show that the lower bound increases when the system is poorly excitable, as characterized by the spectrum of the controllability gramian of the system mapping the noise to the state and the H-infinity norm of the system mapping the input to the state. We further show that for some classes of systems, the lower bound may be exponential in the state dimension, demonstrating exponential sample complexity for learning the linear-quadratic regulator. Show more
Publication status
publishedExternal links
Book title
2023 62nd IEEE Conference on Decision and Control (CDC)Pages / Article No.
Publisher
IEEEEvent
Organisational unit
02650 - Institut für Automatik / Automatic Control Laboratory
Notes
Conference lecture held on December 14, 2023.More
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ETH Bibliography
yes
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