Bayesian Optimization (BO) has emerged as a powerful tool for optimizing unknown and expensive functions while operating under the constraint of limited evaluations. Traditional BO methods often optimize an acquisition function to balance the exploration-exploitation trade-off for sampling. However, most acquisition functions linearly aggregate the exploration and exploitation objectives and strongly rely on the performance of the surrogate model. Additionally, obtaining analytical expressions for acquisition functions is often challenging or impractical in batch evaluation settings. In this paper, we built upon the existing alternative direction to balance the exploration and exploitation objectives; Pareto sampling. Although Pareto sampling has been used within the context of BO, strategies for selecting from the Pareto front for batch settings have not been fully investigated. Focusing on the single objective Bayesian Optimization, we first investigate the existing techniques to select from the Pareto front and then propose a new approach called "Pareto Powered Sampling (Sort/Vol)". By maintaining a diverse set of Pareto-optimal solutions, our method ensures robustness against local optima and facilitates efficient convergence to the global optimum. We demonstrate the effectiveness of Pareto Powered Sampling (PPS) through experiments on benchmark functions and real-world optimization problems. Our results showcase significant improvements in convergence speed and solution quality compared to standard Bayesian Optimization methods.
Nezami et al. (2024) studied this question.