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We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory.
Rates of Convergence for Empirical Processes of Stationary Mixing Sequences
Bin Yu · 1994
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Finite Sample Properties of System Identification Methods
Marco C Campi and Erik Weyer · 2002
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A learning theory approach to system identification and stochastic adaptive control
Mathukumalli Vidyasagar and Rajeeva L Karandikar · 2008
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Hanson-Wright Inequality and sub-Gaussian Concentration
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Introduction to the Non-Asymptotic Analysis of Random Matrices
Roman Vershynin · 2011
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Linear System Identification via Atomic Norm Regularization
Parikshit Shah, Badri Narayan Bhaskar, Gongguo Tang, and Benjamin Recht · 2012
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Concentration Inequalities: A Nonasymptotic Theory of Independence
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Daniel Hsu, Sham M. Kakade, and Tong Zhang · 2014
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Learning without Concentration
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Representation Theory of Semisimple Groups: An Overview Based on Examples (PMS-36)
Anthony W Knapp · 2016
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Learning Linear Dynamical Systems via Spectral Filtering
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Generalization Bounds for Non-Stationary Mixing Processes
Vitaly Kuznetsov and Mehryar Mohri · 2017
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Nonparametric Risk Bounds for Time-Series Forecasting
Daniel J. McDonald, Cosma R. Shalizi, and Mark Schervish · 2017
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Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification
Stephen Tu, Ross Boczar, Andrew Packard, and Benjamin Recht · 2017
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Spectral Filtering for General Linear Dynamical Systems
Elad Hazan, Holden Lee, Karan Singh, Cyril Zhang, and Yi Zhang · 2018
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Concentration Bounds for Single Parameter Adaptive Control
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Sarah Dean, Horia Mania, Nikolai Matni, Benjamin Recht, and Stephen Tu · 2017
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Finite Time Identification in Unstable Linear Systems
Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, and George Michailidis
Cited in the paper.
Finite Time Analysis of Optimal Adaptive Policies for Linear-Quadratic Systems
Mohamad Kazem Shirani Faradonbeh, Ambuj Tewari, and George Michailidis
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Stability Bounds for Non-i.i.d. Processes
Mehryar Mohri and Afshin Rostamizadeh
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Rademacher Complexity Bounds for Non-I.I.D. Processes
Mehryar Mohri and Afshin Rostamizadeh
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Anders Rantzer · 2018
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