Quality or Quantity? Error-Informed Selective Online Learning With Gaussian Processes in Multi-Agent Systems

Zewen Yang; Xiaobing Dai; Jiajun Cheng; Yulong Huang; Peng Shi

doi:10.1109/JAS.2025.125993

Volume 13 Issue 6

Jun. 2026

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 18.3, Top 1 (SCI Q1)

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2026 > 13(6): 1325-1338

Z. Yang, X. Dai, J. Cheng, Y. Huang, and P. Shi, “Quality or quantity? Error-informed selective online learning with gaussian processes in multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1325–1338, Jun. 2026. doi: 10.1109/JAS.2025.125993

Citation:

Z. Yang, X. Dai, J. Cheng, Y. Huang, and P. Shi, “Quality or quantity? Error-informed selective online learning with gaussian processes in multi-agent systems,” IEEE/CAA J. Autom. Sinica, vol. 13, no. 6, pp. 1325–1338, Jun. 2026. doi: 10.1109/JAS.2025.125993

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Quality or Quantity? Error-Informed Selective Online Learning With Gaussian Processes in Multi-Agent Systems

doi: 10.1109/JAS.2025.125993

Funds: This work was supported by the Federal Ministry of Research, Technology, and Space of Germany in the Programme of “Souverän Digital Vernetzt” Under Joint Project 6G-life With Project (16KIS2414) and the National Natural Science Foundation of China (U24B20184, 62373118)

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Author Bio:
Zewen Yang (Member, IEEE) received the M.S. degree in control engineering from Northeast Forest University in 2017. He pursued the Ph.D. degree in control science and engineering at the College of Intelligent Systems Science and Engineering, Harbin Engineering University from 2017 to 2019 and joined the Chair of Information-oriented Control, School of Computation, Information and Technology, the Technical University of Munich (TUM), Munich, Germany, in machine learning and data-driven control until 2023. From 2023 to 2025, he was a postdoctoral researcher at the Robert Koch Institute, Berlin, Germany. Since 2025, he has been with the Chair of Robotics and Systems Intelligence at the Munich Institute of Robotics and Machine Intelligence, TUM. His current research interests include multi-agent systems, cooperative learning, generative models, control theory, and general robotics

Xiaobing Dai received the B.Sc. mechanical engineering from Tongji University in 2018. He received double M.Sc degrees in mechanical engineering, mechatronics and robotics from the Technical University of Munich, Munich, Germany, in 2021. Since February 2022, he is a Ph.D. student at the Chair of Information-oriented Control, TUM School of Computation, Information and Technology at the Technical University of Munich, Munich, Germany. His current research interests include efficient machine learning, networked control systems, and safe learning-based control

Jiajun Cheng received the B.S. degree in automation from the College of Intelligent Systems Science and Engineering, Harbin Engineering University in 2022, where he is currently working toward the Ph.D. degree in control science and engineering. His current research interests include information fusion, robust state estimation, adaptive Kalman filter, and cooperative navigation

Yulong Huang (Senior Member, IEEE) received the B.S. degree in automation from the College of Automation, Harbin Engineering University in 2012. He received the Ph.D degree in control science and engineering from the College of Automation, Harbin Engineering University in 2018. From Nov. 2016 to Nov. 2017, he was a Visiting Graduate Researcher in the Electrical Engineering Department, Columbia University, New York, USA. From December 2019 to December 2021, he was associated with the Department of Mechanical Engineering, City University of Hong Kong, Hong Kong, China, as a Hong Kong Scholar. He is a Full Professor of navigation, guidance, and control at Harbin Engineering University (HEU). His current research interests include state estimation, intelligent information fusion and their applications in navigation technology, such as inertial navigation, integrated navigation, intelligent navigation, and cooperative navigation. Currently, he serves as an Associate Editor for the IEEE Transactions on Automatic Control, the IEEE Transactions on Aerospace and Electronic Systems, the IEEE Aerospace and Electronic Systems Magazine, the IEEE Transactions on Automation Science and Engineering, the IEEE Transactions on Instrumentation and Measurement, and the IEEE Sensors Journal, and a Youth Editor for the IEEE/CAA Journal of Automatica Sinica (JAS), the Satellite Navigation. He was the recipient of the 2018 IEEE Barry Carlton Award from IEEE Transactions on Aerospace and Electronic Systems in 2022, the Honorable Mention of 2017 IEEE Barry Carlton Award from IEEE Transactions on Aerospace and Electronic Systems in 2021, the Best Paper Award of 2024 IEEE International Conference on Unmanned Systems (IEEE ICUS 2024), the Best Paper Award of 2024 IEEE Conference on Energy Internet and Energy System Integration (IEEE EI2 2024), the Best Student Paper Award of 2023 IEEE International Conference on Mechatronics and Automation (IEEE ICMA 2023), and the Best Paper Award of 2021 International Conference on Autonomous Unmanned Systems (ICAUS 2021). He was also the recipient of the Youth Science Award of the Ministry of Education in 2025, the First Prize of Heilongjiang Provincial Natural Science Award (Ranked the 2nd) in 2024, the First Prize of Natural Science Award of Chinese Association of Automation (Ranked the 2nd) in 2021, the Wu Wen-Jun AI Excellent Youth Scholar Award in 2021, the excellent doctoral thesis from Chinese Association of Automation (CAA) in 2019. He was an outstanding Associate Editor and Reviewer for the IEEE Transactions on Instrumentation and Measurement

Peng Shi (Fellow, IEEE) received the Ph.D. degree in electrical engineering from the University of Newcastle, Newcastle, NSW, Australia, in 1994, the Ph.D. degree in mathematics from the University of South Australia, Adelaide, SA, Australia, in 1998, the D.Sc. degree from the University of Glamorgan, Pontypridd, U.K., in 2006, and the D.Eng. degree from Adelaide University, Adelaide, SA, Australia, in 2015. He is currently a Professor with Adelaide University. His research interests include systems and control theory and applications to autonomous and robotic systems, network systems, and cyber-physical systems. Dr. Shi is the Editor-in-Chief of IEEE Transactions on Cybernetics, the Senior Editor of IEEE Access, the Distinguished Lecturer of IEEE SMC Society. He is a Fellow of Australian Academy of Technological Sciences and Engineering, Engineering Academy of Japan, Academy of Europe, and a Fellow of IEEE, IET, IEA and CAA
Corresponding author: Xiaobing Dai, e-mail: xiaobing.dai@tum.de; Yulong Huang, e-mail: huangyl@hrbeu.edu.cn
Received Date: 2025-04-02
Revised Date: 2025-06-26
Accepted Date: 2025-10-17

Abstract

Abstract

Effective cooperation is pivotal in distributed learning for multi-agent systems, where the interplay between the quantity and quality of the machine learning models is crucial. This paper reveals the irrationality of indiscriminate inclusion of all models on agents for joint prediction, highlighting the imperative to prioritize quality over quantity in cooperative learning. Specifically, we present the first selective online learning framework for distributed Gaussian process (GP) regression, namely distributed error-informed GP (EIGP), that enables each agent to assess its neighboring collaborators, using the proposed selection function to choose the higher quality GP models with less prediction errors. Moreover, algorithmic enhancements are embedded within the EIGP, including a greedy algorithm (gEIGP) for accelerating prediction and an adaptive algorithm (aEIGP) for improving prediction accuracy. In addition, approaches for fast prediction and model update are introduced in conjunction with the error-informed quantification term iteration and a data deletion strategy to achieve real-time learning operations. Numerical simulations are performed to demonstrate the effectiveness of the developed methodology, showcasing its superiority over the state-of-the-art distributed GP methods with different benchmarks.
- Adaptive algorithm,
- cooperative learning,
- distributed learning,
- Gaussian process regression,
- greedy algorithm,
- multi-agent system

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¹ The generalization of aEIGP and its variations are presented in Appendix A.

² Codes and datasets are all available at https://github.com/Zewen-Yang/EIGP.

³ For additional results, refer to the extended version [36].

References(38)

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