PAC-Bayesian Meta-Learning for Few-Shot Identification of Linear Dynamical Systems

TMLR Paper7277 Authors

Abstract:

Identifying linear time-invariant (LTI) dynamical systems from data is especially challenging when trajectories are short, noisy, or high-dimensional. Traditional system identification methods typically treat each system in isolation and therefore discard shared information that may exist across related systems. We propose a PAC-Bayesian Meta-Learning framework for LTI system identification (PBML-LTI) that explicitly leverages cross-task structure while preserving task-level heterogeneity. Each task corresponds to an unknown LTI system, and a meta-learner uses a collection of training trajectories to learn a data-dependent prior over system parameters. Given a new system with limited trajectory data, the method performs Bayesian inference to produce a posterior distribution over the new system’s parameters, enabling calibrated uncertainty quantification and principled adaptation in the few-shot regime.

A key technical challenge is temporal dependence: trajectories generated by LTI systems violate i.i.d. assumptions underlying standard learning theory. To address this, we develop generalization guarantees for meta-learned priors under sequential dependence using martingale-based PAC-Bayes analysis with sub-normalized concentration tools. The resulting bounds characterize how the quality of the learned prior controls expected identification error on unseen systems, with explicit dependence on trajectory length, noise, and the divergence between task posteriors and the meta-prior. This connects uncertainty-aware meta-identification with finite-sample theory for dependent dynamical data.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Fredrik_Daniel_Johansson1

Submission Number: 7277