A finite-sample generalization bound for stable LPV systems

Daniel Racz, Martin Gonzalez, Mihaly Petreczky, Andras Benczur, Balint Daroczy
5/16/2024
cs.LGeess.SY

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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.

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Cite this paper

@article{racz2024finitesample,
  title  = {A finite-sample generalization bound for stable LPV systems},
  author = {Daniel Racz and Martin Gonzalez and Mihaly Petreczky and Andras Benczur and Balint Daroczy},
  year   = {2024},
  eprint = {2405.10054},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2405.10054v3}
}

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