mlsanityData to 7 Oct 2026

Learning Linear Dynamics from Bilinear Observations

arXiv 2409.16499 ↗First posted 24 Sep 2024cs.LG cs.SY eess.SYcited by 6

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Abstract (arXiv)

We consider the problem of learning a realization of a partially observed dynamical system with linear state transitions and bilinear observations. Under very mild assumptions on the process and measurement noises, we provide a finite time analysis for learning the unknown dynamics matrices (up to a similarity transform). Our analysis involves a regression problem with heavy-tailed and dependent data. Moreover, each row of our design matrix contains a Kronecker product of current input with a history of inputs, making it difficult to guarantee persistence of excitation. We overcome these challenges, first providing a data-dependent high probability error bound for arbitrary but fixed inputs. Then, we derive a data-independent error bound for inputs chosen according to a simple random design. Our main results provide an upper bound on the statistical error rates and sample complexity of learning the unknown dynamics matrices from a single finite trajectory of bilinear observations.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 42 of its 62 references that are in the map. First posted on arXiv 24 Sep 2024.

Builds on

42 of 62 references.

References · 42

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30 more
  1. 2019Bilinear Bandits with Low-rank Structurecited by 54
  2. 2017Learning Linear Dynamical Systems via Spectral Filteringcited by 46
  3. 2020Logarithmic Regret Bound in Partially Observable Linear Dynamical Systemscited by 46
  4. 2020Non-asymptotic and Accurate Learning of Nonlinear Dynamical Systemscited by 39
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  22. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 4
  2. 2025Sub-optimality of the Separation Principle for Quadratic Control from Bilinear Observationscited by 2
  3. 2025Explore-then-Commit for Nonstationary Linear Bandits with Latent Dynamicscited by 2
  4. 2026Dual Control of Linear Systems from Bilinear Observations with Belief Space Model Predictive Controlcited by 0
  5. 2026Learning Linear Systems under Heavy-Tailed Noise: A Non-Asymptotic Analysis from A Single Trajectorycited by 0
  6. 2026Block Optimism for Nonstationary Bandits with Latent Linear Dynamicscited by 0