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Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimator

arXiv 2003.07937 ↗First posted 17 Mar 2020math.ST cs.LG cs.SYcited by 26

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Abstract (arXiv)

We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory) sufficient for the OLS estimator to be (varepsilon,δ)-PAC, i.e., to yield an estimation error less than varepsilon with probability at least 1-δ. We show that this number matches existing sample complexity lower bounds [1,2] up to universal multiplicative factors (independent of (varepsilon,δ) and of the system). This paper hence establishes the optimality of the OLS estimator for stable systems, a result conjectured in [1]. Our analysis of the performance of the OLS estimator is simpler, sharper, and easier to interpret than existing analyses. It relies on new concentration results for the covariates matrix.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Mar 2020.

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Citing papers per year: 2021: 1; 2022: 10; 2023: 6; 2024: 2; 2025: 3; 2026: 4.

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  5. 2023Exact Recovery for System Identification with More Corrupt Data than Clean Datacited by 2
  6. 2022Online greedy identification of linear dynamical systemscited by 1
  7. 2023SAMoSSA: Multivariate Singular Spectrum Analysis with Stochastic Autoregressive Noisecited by 1
  8. 2025Federated Nonlinear System Identificationcited by 1
  9. 2024Joint Learning of Linear Dynamical Systems under Smoothness Constraintscited by 0
  10. 2025Symmetric Linear Dynamical Systems are Learnable from Few Observationscited by 0
  11. 2026Optimal Centered Active Excitation in Linear System Identificationcited by 0
  12. 2026CLT-Optimal Parameter Error Bounds for Linear System Identificationcited by 0
  13. 2026A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systemscited by 0
  14. 2026Learning Fractional-Order Dynamics from a Single Trajectorycited by 0