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Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems

arXiv 2412.04157 ↗First posted 5 Dec 2024eess.SY cs.LG cs.SYcited by 0

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Abstract (arXiv)

We investigate the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems. Specifically, we consider nonlinear systems with linearly parametrised uncertainty and additive i.i.d. process noise, in feedback with a control policy that is intentionally perturbed by an exploratory input. Assuming the open-loop dynamics satisfy a particular sub-exponential input-to-state growth property, and a region of the state space produces informative data, we establish non-asymptotic guarantees on the estimation error at times when the state trajectory evolves in this region. If the whole state space is informative, high-probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis beyond existing works.

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References · 19

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2020Naive Exploration is Optimal for Online LQRcited by 111
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  11. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
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7 more
  1. 2021Linear Systems can be Hard to Learncited by 20
  2. 2019A Tutorial on Concentration Bounds for System Identificationcited by 19
  3. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  4. 2024Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guaranteescited by 7
  5. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  6. 2022Learning-Based Adaptive Control for Stochastic Linear Systems with Input Constraintscited by 3
  7. 2023Stability Bounds for Learning-Based Adaptive Control of Discrete-Time Multi-Dimensional Stochastic Linear Systems with Input Constraintscited by 2

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