On the Hardness of Learning to Stabilize Linear Systems

• URL: http://arxiv.org/abs/2311.11151v1
• Date: Sat, 18 Nov 2023 19:34:56 GMT
• Title: On the Hardness of Learning to Stabilize Linear Systems
• Authors: Xiong Zeng, Zexiang Liu, Zhe Du, Necmiye Ozay, Mario Sznaier
• Abstract summary: We study the statistical hardness of learning to stabilize linear time-invariant systems. We present a class of systems that can be easy to identify, thanks to a non-degenerate noise process. We tie this result to the hardness of co-stabilizability for this class of systems using ideas from robust control.
• Score: 4.962316236417777
• License: http://creativecommons.org/licenses/by/4.0/
• 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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