Online Learning and Coverage of Unknown Fields Using Random-Feature Gaussian Processes

Ruijie Du, Ruoyu Lin, Yanning Shen, Magnus B. Egerstedt
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1483-1511, 2026.

Abstract

This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) which enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. The incremental update mechanism of O-RFGP naturally supports time-varying environments, allowing efficient adaptation without retaining historical data. Furthermore, to the best of our knowledge, we provide the first theoretical analysis of online learning and coverage through a regret-based formulation, establishing asymptotic no-regret guarantees in the time-invariant setting. The effectiveness of the proposed framework is demonstrated through simulations with both time-invariant and time-varying density functions, along with a physical experiment with a time-varying density function.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-du26a, title = {Online Learning and Coverage of Unknown Fields Using Random-Feature Gaussian Processes}, author = {Du, Ruijie and Lin, Ruoyu and Shen, Yanning and Egerstedt, Magnus B.}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1483--1511}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/du26a/du26a.pdf}, url = {https://proceedings.mlr.press/v331/du26a.html}, abstract = {This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) which enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. The incremental update mechanism of O-RFGP naturally supports time-varying environments, allowing efficient adaptation without retaining historical data. Furthermore, to the best of our knowledge, we provide the first theoretical analysis of online learning and coverage through a regret-based formulation, establishing asymptotic no-regret guarantees in the time-invariant setting. The effectiveness of the proposed framework is demonstrated through simulations with both time-invariant and time-varying density functions, along with a physical experiment with a time-varying density function.} }
Endnote
%0 Conference Paper %T Online Learning and Coverage of Unknown Fields Using Random-Feature Gaussian Processes %A Ruijie Du %A Ruoyu Lin %A Yanning Shen %A Magnus B. Egerstedt %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-du26a %I PMLR %P 1483--1511 %U https://proceedings.mlr.press/v331/du26a.html %V 331 %X This paper proposes a framework for multi-robot systems to perform simultaneous learning and coverage of a domain of interest characterized by an unknown and potentially time-varying density function. To overcome the limitations of Gaussian Process (GP) regression, we employ Random Feature GP (RFGP) and its online variant (O-RFGP) which enables online and incremental inference. By integrating these with Voronoi-based coverage control and Upper Confidence Bound (UCB) sampling strategy, a team of robots can adaptively focus on important regions while refining the learned spatial field for efficient coverage. The incremental update mechanism of O-RFGP naturally supports time-varying environments, allowing efficient adaptation without retaining historical data. Furthermore, to the best of our knowledge, we provide the first theoretical analysis of online learning and coverage through a regret-based formulation, establishing asymptotic no-regret guarantees in the time-invariant setting. The effectiveness of the proposed framework is demonstrated through simulations with both time-invariant and time-varying density functions, along with a physical experiment with a time-varying density function.
APA
Du, R., Lin, R., Shen, Y. & Egerstedt, M.B.. (2026). Online Learning and Coverage of Unknown Fields Using Random-Feature Gaussian Processes. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1483-1511 Available from https://proceedings.mlr.press/v331/du26a.html.

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