Bayesian optimization (BO) is a powerful framework for optimizing black-box, expensive-to-evaluate functions. Over the past decade, many algorithms have been proposed to integrate cheaper, lower-fidelity approximations of the objective function into the optimization process, with the goal of converging towards the global optimum at a reduced cost. This task is generally referred to as multi-fidelity Bayesian optimization (MFBO). However, MFBO algorithms can lead to higher optimization costs than their vanilla BO counterparts, especially when the low-fidelity sources are poor approximations of the objective function, therefore defeating their purpose. To address this issue, we propose rMFBO (robust MFBO), a methodology to make any GP-based MFBO scheme robust to the addition of unreliable information sources. rMFBO comes with a theoretical guarantee that its performance can be bound to its vanilla BO analog, with high controllable probability. We demonstrate the effectiveness of the proposed methodology on a number of numerical benchmarks, outperforming earlier MFBO methods on unreliable sources. We expect rMFBO to be particularly useful to reliably include human experts with varying knowledge within BO processes.

翻译：贝叶斯优化（BO）是一种针对黑箱、评估代价高昂的函数进行优化的强大框架。过去十年中，许多算法被提出以将目标函数的更廉价、低保真度近似纳入优化过程，旨在以更低的成本收敛至全局最优解。这一任务通常被称为多保真度贝叶斯优化（MFBO）。然而，MFBO算法可能比其标准版BO对应方法导致更高的优化成本，尤其是当低保真度源对目标函数的近似效果较差时，这反而违背了其设计初衷。为解决这一问题，我们提出了rMFBO（鲁棒MFBO）方法，该方案能使任何基于高斯过程的MFBO框架对不可靠信息源的加入具有鲁棒性。rMFBO具备理论保障：其性能可被约束于标准版BO对应方法的性能范围内，且具有可控的高概率。我们在多个数值基准测试中验证了该方法的有效性，在不可靠信息源上优于早期MFBO方法。我们预期rMFBO在贝叶斯优化过程中需可靠整合知识水平各异的人类专家时将尤为实用。