Kernel-Based Optimal Control: An Infinitesimal Generator Approach

Petar Bevanda, Nicolas Hoischen, Tobias Wittmann, Jan Brudigam, Sandra Hirche, Boris Houska
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1038-1052, 2025.

Abstract

This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-bevanda25a, title = {Kernel-Based Optimal Control: An Infinitesimal Generator Approach}, author = {Bevanda, Petar and Hoischen, Nicolas and Wittmann, Tobias and Brudigam, Jan and Hirche, Sandra and Houska, Boris}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1038--1052}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/bevanda25a/bevanda25a.pdf}, url = {https://proceedings.mlr.press/v283/bevanda25a.html}, abstract = {This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.} }
Endnote
%0 Conference Paper %T Kernel-Based Optimal Control: An Infinitesimal Generator Approach %A Petar Bevanda %A Nicolas Hoischen %A Tobias Wittmann %A Jan Brudigam %A Sandra Hirche %A Boris Houska %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-bevanda25a %I PMLR %P 1038--1052 %U https://proceedings.mlr.press/v283/bevanda25a.html %V 283 %X This paper presents a novel operator-theoretic approach for optimal control of nonlinear stochastic systems within reproducing kernel Hilbert spaces. Our learning framework leverages data samples of system dynamics and stage cost functions, with only control penalties and constraints provided. The proposed method directly learns the infinitesimal generator of a controlled stochastic diffusion in an infinite-dimensional hypothesis space. We demonstrate that our approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions, enabling a data-driven solution to the optimal control problems. Furthermore, our learning framework includes nonparametric estimators for uncontrolled infinitesimal generators as a special case. Numerical experiments, ranging from synthetic differential equations to simulated robotic systems, showcase the advantages of our approach compared to both modern data-driven and classical nonlinear programming methods for optimal control.
APA
Bevanda, P., Hoischen, N., Wittmann, T., Brudigam, J., Hirche, S. & Houska, B.. (2025). Kernel-Based Optimal Control: An Infinitesimal Generator Approach. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1038-1052 Available from https://proceedings.mlr.press/v283/bevanda25a.html.

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