In many applications, ranging from logistics to engineering, a designer is faced with a sequence of optimization tasks for which the objectives are in the form of black-box functions that are costly to evaluate. Furthermore, higher-fidelity evaluations of the optimization objectives often entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information about the optimal value or the optimal solution for the current task. Assuming that successive optimization tasks are related, this paper introduces a novel information-theoretic acquisition function that balances the need to acquire information about the current task with the goal of collecting information transferable to future tasks. The proposed method transfers across tasks distributions over parameters of a Gaussian process surrogate model by implementing particle-based variational Bayesian updates. Theoretical insights based on the analysis of the expected regret substantiate the benefits of acquiring transferable knowledge across tasks. Furthermore, experimental results across synthetic and real-world examples reveal that the proposed acquisition strategy that caters to future tasks can significantly improve the optimization efficiency as soon as a sufficient number of tasks is processed.

翻译：在从物流到工程等诸多应用领域中，设计者常面临一系列优化任务，其目标函数表现为评估成本高昂的黑箱函数。此外，对优化目标进行更高保真度的评估往往需要更大的成本。现有的多保真度黑箱优化策略通过选择候选解和保真度水平，以最大化当前任务最优值或最优解的信息获取为目标。本文假设连续优化任务之间存在关联性，提出了一种新颖的信息论采集函数，该函数在获取当前任务信息与收集可迁移至未来任务的信息之间实现平衡。所提方法通过实施基于粒子的变分贝叶斯更新，实现了高斯过程代理模型参数分布在任务间的迁移。基于期望遗憾分析的理论研究证实了跨任务获取可迁移知识的优势。此外，在合成与真实案例中的实验结果表明，所提出的面向未来任务的采集策略在处理足够数量的任务后，能显著提升优化效率。