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<p>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 a weighted <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\text { H}_{\text { 2}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mspace width="0.333333em" /> <msub> <mtext>H</mtext> <mrow> <mspace width="0.333333em" /> <mtext>2</mtext> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation>-like norm of the chosen class of the LPV systems, but does not depend on the time interval for which the signals are considered.</p>

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A finite-sample generalization bound for stable LPV systems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月8日

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  • Dániel Rácz,
  • Martin Gonzalez,
  • Mihály Petreczky,
  • András Benczúr,
  • Bálint Daróczy

摘要

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 a weighted \(\text { H}_{\text { 2}}\) H 2 -like norm of the chosen class of the LPV systems, but does not depend on the time interval for which the signals are considered.