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：本文研究一类评估代价高昂的黑箱函数优化问题，其中可通过并行方式获取含噪声的函数值。针对该问题，并行贝叶斯优化（PBO）是一种具有前景的解决方案，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目标。然而，现有PBO方法存在实际性能不佳或缺乏理论保证的局限性。本研究提出一种基于经典克里金置信启发式策略的PBO方法——随机克里金置信法，该方法继承了原始KB策略的四大优势：低计算复杂度、简易实现性、对各类BO方法的广泛适用性，以及异步并行化的兼容性。进一步地，我们证明随机克里金置信法能够实现贝叶斯期望遗憾的理论保证。通过在合成函数、基准测试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。