mlsanityData to 7 Oct 2026

Learning Dynamical Systems by Leveraging Data from Similar Systems

arXiv 2302.04344 ↗First posted 8 Feb 2023stat.ML cs.LG cs.SYcited by 8

Not on the map. Why?

Abstract (arXiv)

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 22 of its 51 references that are in the map. First posted on arXiv 8 Feb 2023.

Builds on

22 of 51 references.

References · 22

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2017On the Sample Complexity of the Linear Quadratic Regulatorcited by 151
  3. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  4. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  5. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 77
  6. 2019Finite Sample Analysis of Stochastic System Identificationcited by 67
  7. 2017Finite Time Identification in Unstable Linear Systemscited by 66
  8. 2019Learning Linear Dynamical Systems with Semi-Parametric Least Squarescited by 58
  9. 2020Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectoriescited by 38
  10. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
  11. 2020Logarithmic Regret for Learning Linear Quadratic Regulators Efficientlycited by 33
  12. 2018Safely Learning to Control the Constrained Linear Quadratic Regulatorcited by 31
10 more
  1. 2020Concentration Inequalities for Statistical Inferencecited by 24
  2. 2022Learning from many trajectoriescited by 24
  3. 2019A Tutorial on Concentration Bounds for System Identificationcited by 19
  4. 2021Joint Learning of Linear Time-Invariant Dynamical Systemscited by 16
  5. 2022Identifying the Dynamics of a System by Leveraging Data from Similar Systemscited by 15
  6. 2019Nonparametric Finite Time LTI System Identificationcited by 11
  7. 2022Learning the Dynamics of Autonomous Linear Systems From Multiple Trajectoriescited by 8
  8. 2021On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structurecited by 7
  9. 2022Data-based Transfer Stabilization in Linear Systemscited by 5
  10. 2022Joint Learning-Based Stabilization of Multiple Unknown Linear Systemscited by 3

Built on by

Cited by year

Citing papers per year: 2023: 4; 2024: 1; 2025: 3.

8 papers.

  1. 2023Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Datacited by 12
  2. 2023Learning Personalized Models with Clustered System Identificationcited by 10
  3. 2023Learning Linearized Models from Nonlinear Systems with Finite Datacited by 3
  4. 2024Combining Federated Learning and Control: A Surveycited by 2
  5. 2023Online Change Points Detection for Linear Dynamical Systems with Finite Sample Guaranteescited by 1
  6. 2025Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datacited by 1
  7. 2025Harnessing Data from Clustered LQR Systems: Personalized and Collaborative Policy Optimizationcited by 1
  8. 2025Adaptive prediction theory combining offline and online learningcited by 0