We consider an optimization problem of an expensive-to-evaluate black-box function, in which we can obtain noisy function values in parallel. For this problem, parallel Bayesian optimization (PBO) is a promising approach, which aims to optimize with fewer function evaluations by selecting a diverse input set for parallel evaluation. However, existing PBO methods suffer from poor practical performance or lack theoretical guarantees. In this study, we propose a PBO method, called randomized kriging believer (KB), based on a well-known KB heuristic and inheriting the advantages of the original KB: low computational complexity, a simple implementation, versatility across various BO methods, and applicability to asynchronous parallelization. Furthermore, we show that our randomized KB achieves Bayesian expected regret guarantees. We demonstrate the effectiveness of the proposed method through experiments on synthetic and benchmark functions and emulators of real-world data.

翻译：我们考虑一个评估代价高昂的黑箱函数优化问题，其中可以并行获取带噪声的函数值。针对该问题，并行贝叶斯优化（PBO）是一种前景广阔的方法，其通过选择多样化的输入集进行并行评估，旨在以更少的函数评估次数实现优化。然而，现有PBO方法存在实际性能不佳或缺乏理论保证的问题。本研究提出一种基于经典KB启发式策略的PBO方法——随机克里金置信者（KB），该方法继承了原始KB的优势：计算复杂度低、实现简单、可适配多种BO方法，并适用于异步并行场景。此外，我们证明随机KB方法能够实现贝叶斯期望遗憾的理论保证。通过在合成函数、基准函数以及真实数据仿真器上的实验，验证了所提方法的有效性。