A finite-sample generalization bound for stable LPV systems
This work addresses a theoretical challenge in dynamical systems learning, offering a new bound for LPV systems, but it appears incremental as it extends existing PAC frameworks to a specific system type.
The paper tackles the problem of providing generalization error bounds for learning stable continuous-time linear parameter-varying (LPV) systems from finite data, deriving a Probably Approximately Correct (PAC) bound that depends on the H2 norm of the system class but not on the time interval.
One of the main theoretical challenges in learning dynamical systems from data is providing upper bounds on the generalization error, that is, the difference between the expected prediction error and the empirical prediction error measured on some finite sample. In machine learning, a popular class of such bounds are the so-called Probably Approximately Correct (PAC) bounds. In this paper, we derive a PAC bound for stable continuous-time linear parameter-varying (LPV) systems. Our bound depends on the H2 norm of the chosen class of the LPV systems, but does not depend on the time interval for which the signals are considered.