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*                          Einladung

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*                     Informatik-Oberseminar

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Zeit:  Dienstag, 25. März 2025, 14.00 Uhr

Ort:   Seminarraum 423, 4. OG, Theaterstraße 35-39, 52062 Aachen

Referent: Christian Martin Fiedler M.Sc.

Institut für Data Science im Maschinenbau (DSME)

Thema: Contributions to Kernel Methods in Systems and Control

Abstract:

Machine learning is increasingly used in systems and control, which is motivated by challenging control, simulation and analysis problems, abundant data and computing resources, as well as impressive theoretical and methodological advances in machine learning. The established class of kernel methods is of particular interest in this context, due to their rich theory, modularity, efficient and reliable algorithms, and indeed kernel methods are frequently used in systems and control. We present two exemplary and complementary contributions to this flourishing field.

First, many learning-based control approaches are based on combining uncertainty bounds for Gaussian process (GP) regression with robust control methods.  We revisit the foundations of this domain by consolidating, improving, and carefully evaluating the required uncertainty bounds, and use them in learning-enhanced control applications. Furthermore, we discuss a severe practical limitation of these approaches, the a priori knowledge of an upper bound on the reproducing kernel Hilbert space (RKHS) norm of the target function, and propose to combine geometric assumptions together with kernel methods as a promising alternative.

Second, we initiate a new research direction by combining kernels with mean field limits as appearing in kinetic theory. Motivated by learning problems on large-scale multiagent systems, we introduce mean field limits of kernels, and provide an extensive theory for the resulting RKHSs. This is used in turn in the analysis of kernel-based statistical learning in the mean field limit, which not only is a novel form of large-scale limit in theoretical machine learning, but provides also a solid foundation for applications in kinetic theory.

Es laden ein: die Dozentinnen und Dozenten der Informatik