Near optimal finite time identification of arbitrary linear dynamical systems
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sarkar19a.pdf
Description
Published version
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773.34 KB
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Unknown
Checksum (MD5)
6aeed81ff2080932217ddc36f03ba0b3
Author(s)
Sarkar, Tuhin
Rakhlin, Alexander
Date Issued
January 2019
Journal
36th International Conference on Machine Learning, ICML 2019
Citation
Sarkar, T and Rakhlin, A. 2019. "Near optimal finite time identification of arbitrary linear dynamical systems." 36th International Conference on Machine Learning, ICML 2019, 2019-June.
Version
Final published version
Abstract
© 2019 International Machine Learning Society (IMLS). Wc derive finite time error bounds for estimating general linear time-invariant (LTI) systems from a single observed trajectory using the method of least squares. We provide the first analysis of the general case when eigenvalues of the LTI system are arbitrarily distributed in three regimes: stable, marginally stable, and explosive. Our analysis yields sharp upper bounds for each of these cases separately. We observe that although the underlying process behaves quite differently in each of these three regimes, the systematic analysis of a self-normalized martingale difference term helps bound identification error up to logarithmic factors of the lower bound. On the other hand, we demonstrate that the least squares solution may be statistically inconsistent under certain conditions even when the signal-to-noise ratio is high.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://proceedings.mlr.press/v97/sarkar19a
