On the Hardness of Learning to Stabilize Linear Systems
Abstract
Inspired by the work of Tsiamis et al. \cite{tsiamis2022learning}, in this paper we study the statistical hardness of learning to stabilize linear time-invariant systems. Hardness is measured by the number of samples required to achieve a learning task with a given probability. The work in \cite{tsiamis2022learning} shows that there exist system classes that are hard to learn to stabilize with the core reason being the hardness of identification. Here we present a class of systems that can be easy to identify, thanks to a non-degenerate noise process that excites all modes, but the sample complexity of stabilization still increases exponentially with the system dimension. We tie this result to the hardness of co-stabilizability for this class of systems using ideas from robust control.
Keywords
Cite
@article{arxiv.2311.11151,
title = {On the Hardness of Learning to Stabilize Linear Systems},
author = {Xiong Zeng and Zexiang Liu and Zhe Du and Necmiye Ozay and Mario Sznaier},
journal= {arXiv preprint arXiv:2311.11151},
year = {2023}
}
Comments
7 pages, 2 figures, accepted by CDC 2023