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：在许多应用领域（从物流到工程）中，设计者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调整不同学习任务的神经网络模型超参数。除直接评估目标函数外，设计者还可获取目标函数的近似形式，其中高保真评估需付出更高成本。现有低保真黑箱优化策略通过选择候选解与保真度水平，旨在最大化当前任务最优值或最优解的信息增益。假设连续优化任务具有相关性，本文提出一种新颖的信息论采集函数，在获取当前任务信息与收集可传递至未来任务的信息之间取得平衡。该方法引入跨任务共享潜变量，并通过基于粒子的变分贝叶斯更新实现任务间传递。合成数据与真实案例的实验结果表明，这种面向未来任务的远见采集策略在处理足够数量的任务后，能显著提升优化效率。