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. For example, the designer may need to tune the hyperparameters of neural network models for different learning tasks over time. Rather than evaluating the objective function for each candidate solution, the designer may have access to approximations of the objective functions, for which higher-fidelity evaluations entail a larger cost. Existing multi-fidelity black-box optimization strategies select candidate solutions and fidelity levels with the goal of maximizing the information accrued about the optimal value or 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 includes shared inter-task latent variables, which are transferred across tasks by implementing particle-based variational Bayesian updates. Experimental results across synthetic and real-world examples reveal that the proposed provident 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：在许多应用场景中，从物流到工程领域，设计者常面临一系列优化任务，其目标函数为评估成本高昂的黑箱函数。例如，设计者可能需要随时间推移为不同学习任务调整神经网络模型的超参数。相较于直接评估每个候选解的目标函数值，设计者往往能够获取目标函数的近似值，其中高保真度评估需要更高成本。现有跨保真度黑箱优化策略通过选择候选解与保真度等级，旨在最大化当前任务中关于最优值或最优解的信息积累。考虑到连续优化任务之间的相关性，本文提出一种新型信息论采集函数，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。该方法包含跨任务共享的隐变量，并通过基于粒子的变分贝叶斯更新实现任务间迁移。合成数据与实际案例的实验结果表明，这种为未来任务预先规划的采集策略在处理足够多的任务后，能够显著提升优化效率。