PMCBO: A Distributed Multi-Task Collaborative Bayesian Optimization Algorithm via Expert Beliefs over Networks

To optimize expensive black-box functions over networks, one of the most dominant frameworks is distributed Bayesian optimization (DBO), where local information can be exchanged among agents. However, DBO suffers from low evaluation efficiency due to limited data in the initial stage and the high cost of evaluations among multiple objectives. To tackle these obstacles, we propose a prior-informed multi-task collaborative Bayesian optimization (PMCBO) algorithm over networks. Concretely, PMCBO integrates expert prior knowledge about the location of optimum into the distributed multi-task Bayesian optimization framework to reduce the cost of evaluations. Meanwhile, PMCBO combines multi-task Bayesian optimization with a collaborative mechanism to improve the evaluation efficiency. Furthermore, we rigorously prove that the cumulative regret bound of PMCBO can achieve sub-linearly with high probability, where the acquisition functions employ expected improvement (EI) and upper-confidence bound (UCB) based on a Gaussian process surrogate. Finally, we implement various experiments to evaluate the effectiveness of PMCBO. The experimental results demonstrate that PMCBO can achieve state-of-the-art performance and benefit all clients based on diverse benchmarks and prior characteristics.