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On the Effect of Instability on Learning Continuous-Time Linear Control Systems

arXiv 2409.11327 ↗First posted 17 Sep 2024stat.ML cs.LGcited by 0

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Abstract (arXiv)

We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly randomized control inputs. Then, we establish theoretical performance guarantees showing that the estimation error decays with trajectory length, a measure of excitability, and the signal-to-noise ratio, while it grows with dimension. Numerical illustrations that showcase the rates of learning the dynamics, will be provided as well. To perform the theoretical analysis, we develop new technical tools that are of independent interest. That includes non-asymptotic stochastic bounds for highly non-stationary martingales and generalized laws of iterated logarithms, among others.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 14 of its 40 references that are in the map. First posted on arXiv 17 Sep 2024.

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14 of 40 references.

References · 14

  1. 2018Time-uniform, nonparametric, nonasymptotic confidence sequencescited by 220
  2. 2020Few-Shot Learning via Learning the Representation, Provablycited by 213
  3. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  4. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  5. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  6. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 77
  7. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  8. 2020Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectoriescited by 38
  9. 2020Logarithmic regret for episodic continuous-time linear-quadratic reinforcement learning over a finite-time horizoncited by 31
  10. 2018Exploration versus exploitation in reinforcement learning: a stochastic control approachcited by 17
  11. 2021Joint Learning of Linear Time-Invariant Dynamical Systemscited by 16
  12. 2019On Applications of Bootstrap in Continuous Space Reinforcement Learningcited by 9
2 more
  1. 2018Optimal consensus control of the Cucker-Smale modelcited by 5
  2. 2021Bayesian Algorithms Learn to Stabilize Unknown Continuous-Time Systemscited by 2

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