1. On the Hardness of Learning to Stabilize Linear Systems
- Author
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Zeng, Xiong, Liu, Zexiang, Du, Zhe, Ozay, Necmiye, and Sznaier, Mario
- Subjects
Electrical Engineering and Systems Science - Systems and Control ,Computer Science - Machine Learning ,Statistics - Machine Learning - 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., Comment: 7 pages, 2 figures, accepted by CDC 2023
- Published
- 2023