mlsanityData to 7 Oct 2026

Finite Sample Identification of Partially Observed Bilinear Dynamical Systems

arXiv 2501.07652 ↗First posted 13 Jan 2025cs.LG cs.SY eess.SYcited by 4

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Abstract (arXiv)

We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the system's Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. Our bilinear system identification algorithm learns the system's Markov-like parameters by regressing the outputs to highly correlated, nonlinear, and heavy-tailed covariates. Moreover, the stability of BLDS depends on the sequence of inputs used to excite the system. These properties, unique to partially observed bilinear dynamical systems, pose significant challenges to the analysis of our algorithm for learning the unknown dynamics. We address these challenges and provide high probability error bounds on our identification algorithm under a uniform stability assumption. Our analysis provides insights into system theoretic quantities that affect learning accuracy and sample complexity. Lastly, we perform numerical experiments with synthetic data to reinforce these insights.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 35 of its 64 references that are in the map. First posted on arXiv 13 Jan 2025.

Builds on

35 of 64 references.

References · 35

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23 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2025Explore-then-Commit for Nonstationary Linear Bandits with Latent Dynamicscited by 2
  2. 2025A finite-sample bound for identifying partially observed linear switched systems from a single trajectorycited by 1
  3. 2025Frequency Response Identification of Low-Order Systems: Finite-Sample Analysiscited by 0
  4. 2026Achieving widetildeO(1/ε) Sample Complexity for Bilinear Systems Identification under Bounded Noisescited by 0