Quality or Quantity? Error-Informed Selective Online Learning with Gaussian Processes in Multi-Agent Systems: Extended Version

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.