  This paper introduces an innovative approach to enhance distributed
cooperative learning using Gaussian process (GP) regression in multi-agent
systems (MASs). The key contribution of this work is the development of an
elective learning algorithm, namely prior-aware elective distributed GP
(Pri-GP), which empowers agents with the capability to selectively request
predictions from neighboring agents based on their trustworthiness. The
proposed Pri-GP effectively improves individual prediction accuracy, especially
in cases where the prior knowledge of an agent is incorrect. Moreover, it
eliminates the need for computationally intensive variance calculations for
determining aggregation weights in distributed GP. Furthermore, we establish a
prediction error bound within the Pri-GP framework, ensuring the reliability of
predictions, which is regarded as a crucial property in safety-critical MAS
applications.
