Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate, and hence admit only small evaluation budgets. BO is particularly popular for solving numerical optimization problems in industry, where the evaluation of objective functions often relies on time-consuming simulations or physical experiments. However, many industrial problems depend on a large number of parameters. This poses a challenge for BO algorithms, whose performance is often reported to suffer when the dimension grows beyond 15 variables. Although many new algorithms have been proposed to address this problem, it is not well understood which one is the best for which optimization scenario. In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at increasing dimensionality, ranging from 10 to 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.

翻译：贝叶斯优化（BO）是一类基于代理模型的黑盒启发式方法，能够高效处理评估代价高昂、因而仅允许较小评估预算的优化问题。BO在工业界的数值优化问题求解中尤为常见，因为此类问题的目标函数评估往往依赖于耗时仿真或物理实验。然而，许多工业问题依赖于大量参数。这给BO算法带来了挑战——其性能常被报道在维度超过15个变量时下降。尽管已提出诸多新算法解决该问题，但目前尚不明确何种算法适用于何种优化场景。本研究在COCO环境的24个BBOB函数上，对五种主流高维BO算法以及朴素BO和CMA-ES进行了对比，维度范围从10个变量至60个变量递增。实验结果验证了在有限评估预算下BO优于CMA-ES，并表明改进BO最有前景的方法是采用信任区域。然而，我们也观察到不同函数景观和预算利用阶段存在显著性能差异，这表明仍有改进空间，例如通过算法组件的混合优化。