<p>This paper proposes a general-purpose multi-agent Bayesian optimization (MABO) where agents are connected via shared variables or constraints, and each agent’s local cost is unknown. The proposed approach is general-purpose in the sense that it can be used with a broad class of decomposition methods, whereby we augment traditional BO acquisition functions with suitably derived coordinating terms to facilitate coordination among subsystems without sharing local data. Regret analysis is also carried out for the general-purpose MABO framework, which reveals that the cumulative regret of the proposed general-purpose MABO is the sum of individual regrets and is independent of the coordinating terms. This adaptability to different decomposition methods ensures versatility across diverse distributed optimization scenarios. Numerical experiments validate the effectiveness of the proposed MABO framework for different classes of decomposition methods.</p>