Subgradient Method for System Identification with Non-Smooth Objectives

Baturalp Yalcin, Jihun Kim, Javad Lavaei
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:2151-2170, 2026.

Abstract

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting, where the optimization problems to be solved evolve over time as new measurements are collected, and we establish linear convergence to the ground-truth system for both the best and Polyak step sizes after a burn-in period. We further characterize sublinear convergence of the iterates under constant and diminishing step sizes, which require only minimal information and thus offer broad applicability. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-yalcin26a, title = {Subgradient Method for System Identification with Non-Smooth Objectives}, author = {Yalcin, Baturalp and Kim, Jihun and Lavaei, Javad}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {2151--2170}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/yalcin26a/yalcin26a.pdf}, url = {https://proceedings.mlr.press/v331/yalcin26a.html}, abstract = {This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting, where the optimization problems to be solved evolve over time as new measurements are collected, and we establish linear convergence to the ground-truth system for both the best and Polyak step sizes after a burn-in period. We further characterize sublinear convergence of the iterates under constant and diminishing step sizes, which require only minimal information and thus offer broad applicability. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.} }
Endnote
%0 Conference Paper %T Subgradient Method for System Identification with Non-Smooth Objectives %A Baturalp Yalcin %A Jihun Kim %A Javad Lavaei %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-yalcin26a %I PMLR %P 2151--2170 %U https://proceedings.mlr.press/v331/yalcin26a.html %V 331 %X This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting, where the optimization problems to be solved evolve over time as new measurements are collected, and we establish linear convergence to the ground-truth system for both the best and Polyak step sizes after a burn-in period. We further characterize sublinear convergence of the iterates under constant and diminishing step sizes, which require only minimal information and thus offer broad applicability. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.
APA
Yalcin, B., Kim, J. & Lavaei, J.. (2026). Subgradient Method for System Identification with Non-Smooth Objectives. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:2151-2170 Available from https://proceedings.mlr.press/v331/yalcin26a.html.

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