  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.
