On the Hardness of Learning to Stabilize Linear Systems

Xiong Zeng, Zexiang Liu, Zhe Du, Necmiye Ozay, Mario Sznaier
11/18/2023
eess.SYcs.LGstat.ML

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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.

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Cite this paper

@article{zeng2023hardness,
  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},
  year   = {2023},
  eprint = {2311.11151},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2311.11151v1}
}

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