This paper studies the problem of distributed multi-agent Bayesian optimization with both coupled black-box constraints and known affine constraints. A primal-dual distributed algorithm is proposed that achieves similar regret/violation bounds as those in the single-agent case for the black-box objective and constraint functions. Additionally, the algorithm guarantees an $\mathcal{O}(N\sqrt{T})$ bound on the cumulative violation for the known affine constraints, where $N$ is the number of agents. Hence, it is ensured that the average of the samples satisfies the affine constraints up to the error $\mathcal{O}({N}/{\sqrt{T}})$. Furthermore, we characterize certain conditions under which our algorithm can bound a stronger metric of cumulative violation and provide best-iterate convergence without affine constraint. The method is then applied to both sampled instances from Gaussian processes and a real-world optimal power allocation problem for wireless communication; the results show that our method simultaneously provides close-to-optimal performance and maintains minor violations on average, corroborating our theoretical analysis.

该研究针对具有耦合黑盒约束和已知仿射约束的分布式多智能体贝叶斯优化问题，提出了一种原始-对偶分布式算法，其与单智能体情况下黑盒目标函数和约束函数的遗憾/违规边界相似。此外，该算法保证了已知仿射约束的累积违规性的O(N√T)界，其中N是智能体数量。因此，平均样本满足仿射约束的误差不超过O(N/√T)。此外，我们确定了某些条件，使得我们的算法能够对累积违规率进行更强的限制，并在没有仿射约束的情况下提供最佳迭代收敛。然后，该方法应用于来自高斯过程的采样实例和无线通信的实际最优功率分配问题；结果表明我们的方法既能提供接近最优的性能，又能保持平均违规性较小，验证了我们的理论分析。

多智能体贝叶斯优化与耦合黑盒和仿射约束