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.

介绍了一种新颖的信息论获取函数，通过实施基于粒子变分贝叶斯更新的共享任务间潜在变量，平衡了对当前任务信息获取需求与收集可迁移到未来任务的信息目标，实验证明，该策略能够显著提高优化效率。

多保真贝叶斯优化与跨任务可转移最大值熵搜索