On the Hardness of Learning to Stabilize Linear Systems
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Abstract (arXiv)
Inspired by the work of Tsiamis et al. citetsiamis2022learning, 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 citetsiamis2022learning 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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 22 of its 36 references that are in the map. First posted on arXiv 18 Nov 2023.
Builds on
22 of 36 references.
References · 22
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