mlsanityData to 14 Oct 2026

Finite Sample Identification of Bilinear Dynamical Systems

arXiv 2208.13915 ↗First posted 29 Aug 2022cs.LG cs.SY eess.SYcited by 12

Not on the map. Why?

Abstract (arXiv)

Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system's states and inputs. Under a mild marginal mean-square stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of the trajectory length, the dimensionality of the system and the input size. Our proof technique relies on an application of martingale small-ball condition. This enables us to correctly capture the properties of the problem, specifically our error rates do not deteriorate with increasing instability. Finally, we show that numerical experiments are well-aligned with our theoretical results.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 22 of its 34 references that are in the map. First posted on arXiv 29 Aug 2022.

Builds on

22 of 34 references.

References · 22

  1. 2018Learning Without Mixing: Towards A Sharp Analysis of Linear System Identificationcited by 158
  2. 2018Near optimal finite time identification of arbitrary linear dynamical systemscited by 89
  3. 2018Regret Bounds for Robust Adaptive Control of the Linear Quadratic Regulatorcited by 86
  4. 2016Gradient Descent Learns Linear Dynamical Systemscited by 79
  5. 2018Non-asymptotic Identification of LTI Systems from a Single Trajectorycited by 78
  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. 2017Learning Linear Dynamical Systems via Spectral Filteringcited by 46
  10. 2020Learning nonlinear dynamical systems from a single trajectorycited by 46
  11. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
  12. 2020Active Learning for Identification of Linear Dynamical Systemscited by 33
10 more
  1. 2020Finite-time Identification of Stable Linear Systems: Optimality of the Least-Squares Estimatorcited by 26
  2. 2022Single Trajectory Nonparametric Learning of Nonlinear Dynamicscited by 26
  3. 2020Regret Bounds for Adaptive Nonlinear Controlcited by 25
  4. 2019Learning Sparse Dynamical Systems from a Single Sample Trajectorycited by 20
  5. 2020Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamicscited by 18
  6. 2021Near-optimal Offline and Streaming Algorithms for Learning Non-Linear Dynamical Systemscited by 17
  7. 2018Stochastic Gradient Descent Learns State Equations with Nonlinear Activationscited by 16
  8. 2021Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Boundscited by 14
  9. 2019Convex Programming for Estimation in Nonlinear Recurrent Modelscited by 7
  10. 2022Efficient learning of hidden state LTI state space models of unknown ordercited by 7

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 4; 2025: 2; 2026: 1.

12 papers.

  1. 2023The noise level in linear regression with dependent datacited by 6
  2. 2023Learning the Uncertainty Sets for Control Dynamics via Set Membership: A Non-Asymptotic Analysiscited by 6
  3. 2024Learning Linear Dynamics from Bilinear Observationscited by 6
  4. 2023Non-asymptotic System Identification for Linear Systems with Nonlinear Policiescited by 5
  5. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 5
  6. 2023PAC-Bayes Generalisation Bounds for Dynamical Systems Including Stable RNNscited by 4
  7. 2024A Tensor Decomposition Perspective on Second-order RNNscited by 3
  8. 2024End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic datacited by 1
  9. 2025High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systemscited by 1
  10. 2022Learning Nonlinear Couplings in Network of Agents from a Single Sample Trajectorycited by 0
  11. 2024Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systemscited by 0
  12. 2026Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noisescited by 0