Finite Sample Identification of Partially Observed Bilinear Dynamical Systems

Yahya Sattar, Yassir Jedra, Maryam Fazel, Sarah Dean
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1271-1285, 2025.

Abstract

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 an algorithm and a finite time analysis for learning the system’s Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. The stability of BLDS depends on the sequence of inputs used to excite the system. Moreover, our identification algorithm regresses the outputs to highly correlated, nonlinear, and heavy-tailed covariates. 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-sattar25a, title = {Finite Sample Identification of Partially Observed Bilinear Dynamical Systems}, author = {Sattar, Yahya and Jedra, Yassir and Fazel, Maryam and Dean, Sarah}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1271--1285}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/sattar25a/sattar25a.pdf}, url = {https://proceedings.mlr.press/v283/sattar25a.html}, abstract = {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 an algorithm and a finite time analysis for learning the system’s Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. The stability of BLDS depends on the sequence of inputs used to excite the system. Moreover, our identification algorithm regresses the outputs to highly correlated, nonlinear, and heavy-tailed covariates. 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.} }
Endnote
%0 Conference Paper %T Finite Sample Identification of Partially Observed Bilinear Dynamical Systems %A Yahya Sattar %A Yassir Jedra %A Maryam Fazel %A Sarah Dean %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-sattar25a %I PMLR %P 1271--1285 %U https://proceedings.mlr.press/v283/sattar25a.html %V 283 %X 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 an algorithm and a finite time analysis for learning the system’s Markov-like parameters, from which a balanced realization of the bilinear system can be obtained. The stability of BLDS depends on the sequence of inputs used to excite the system. Moreover, our identification algorithm regresses the outputs to highly correlated, nonlinear, and heavy-tailed covariates. 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.
APA
Sattar, Y., Jedra, Y., Fazel, M. & Dean, S.. (2025). Finite Sample Identification of Partially Observed Bilinear Dynamical Systems. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1271-1285 Available from https://proceedings.mlr.press/v283/sattar25a.html.

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