Bayesian optimization (BO) is widely used to optimize expensive-to-evaluate black-box functions.BO first builds a surrogate model to represent the objective function and assesses its uncertainty. It then decides where to sample by maximizing an acquisition function (AF) based on the surrogate model. However, when dealing with high-dimensional problems, finding the global maximum of the AF becomes increasingly challenging. In such cases, the initialization of the AF maximizer plays a pivotal role, as an inadequate setup can severely hinder the effectiveness of the AF. This paper investigates a largely understudied problem concerning the impact of AF maximizer initialization on exploiting AFs' capability. Our large-scale empirical study shows that the widely used random initialization strategy often fails to harness the potential of an AF. In light of this, we propose a better initialization approach by employing multiple heuristic optimizers to leverage the historical data of black-box optimization to generate initial points for the AF maximize. We evaluate our approach with a range of heavily studied synthetic functions and real-world applications. Experimental results show that our techniques, while simple, can significantly enhance the standard BO and outperform state-of-the-art methods by a large margin in most test cases.

翻译：贝叶斯优化被广泛用于优化评估代价高昂的黑箱函数。它首先构建一个代理模型以表示目标函数并评估其不确定性，然后基于代理模型通过最大化采集函数来决定采样位置。然而，在处理高维问题时，寻找采集函数的全局最大值变得愈发困难。在此类场景中，采集函数最大化器的初始化起着关键作用，因为不当的设置会严重削弱采集函数的效果。本文研究了关于采集函数最大化器初始化对其能力影响的一个长期被忽视的问题。我们的大规模实证研究表明，广泛使用的随机初始化策略往往无法充分发挥采集函数的潜力。据此，我们提出了一种更好的初始化方法，通过采用多种启发式优化器利用黑箱优化历史数据来生成采集函数最大化器的初始点。我们通过一系列广泛研究的合成函数和实际应用评估了该方法。实验结果表明，我们的技术虽然简单，但能显著增强标准贝叶斯优化，并在大多数测试案例中以较大优势超越当前最先进的方法。