Bayesian optimisation provides an effective method to optimise expensive black box functions. It has recently been applied to problems in fluid dynamics. This paper studies and compares common Bayesian optimisation algorithms empirically on a range of synthetic test functions. It investigates the choice of acquisition function and number of training samples, exact calculation of acquisition functions and Monte Carlo based approaches and both single-point and multi-point optimisation. The test functions considered cover a wide selection of challenges and therefore serve as an ideal test bed to understand the performance of Bayesian optimisation and to identify general situations where Bayesian optimisation performs well and poorly. This knowledge can be utilised in applications, including those in fluid dynamics, where objective functions are unknown. The results of this investigation show that the choices to be made are less relevant for relatively simple functions, while optimistic acquisition functions such as Upper Confidence Bound should be preferred for more complex objective functions. Furthermore, results from the Monte Carlo approach are comparable to results from analytical acquisition functions. In instances where the objective function allows parallel evaluations, the multi-point approach offers a quicker alternative, yet it may potentially require more objective function evaluations.
翻译:Bayesian优化是优化昂贵黑盒功能的有效方法,最近已应用于流体动态问题。本文研究并用经验对一系列合成测试功能的通用Bayesian优化算法进行了比较;调查了获取功能的选择和培训样本的数量、获取功能的精确计算和蒙特卡洛办法,以及单点和多点优化办法;认为测试功能包括广泛的挑战选择,因此是了解Bayesian优化业绩和查明Bayesian优化表现良好和不良的一般情况的理想测试床;这一知识可用于应用中,包括流动动态功能未知的应用中;调查结果表明,对于相对简单的功能,选择的关联性较小,而对于更复杂的客观功能,则更倾向于采用超信任机制等乐观的获取功能;此外,蒙特卡洛办法的结果与分析获取功能的结果相近。在客观功能允许平行评估的情况下,多点方法提供了更快捷的替代方法,但可能需要更客观的功能评估。