A finite-sample generalization bound for stable LPV systems

TL;DR

This paper derives a PAC generalization bound for stable continuous-time LPV systems, linking the bound to the H2 norm and providing insights into the system's learnability from finite data samples.

Contribution

It introduces a novel PAC bound for stable LPV systems that depends on the H2 norm and is independent of the time interval, advancing theoretical understanding.

Findings

The PAC bound depends on the H2 norm of LPV systems.

The bound is independent of the time interval considered.

Provides a theoretical guarantee for learning LPV systems from finite data.

Abstract

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.