  Bayesian optimization (BO) is a popular framework to optimize black-box
functions. In many applications, the objective function can be evaluated at
multiple fidelities to enable a trade-off between the cost and accuracy. To
reduce the optimization cost, many multi-fidelity BO methods have been
proposed. Despite their success, these methods either ignore or over-simplify
the strong, complex correlations across the fidelities, and hence can be
inefficient in estimating the objective function. To address this issue, we
propose Deep Neural Network Multi-Fidelity Bayesian Optimization (DNN-MFBO)
that can flexibly capture all kinds of complicated relationships between the
fidelities to improve the objective function estimation and hence the
optimization performance. We use sequential, fidelity-wise Gauss-Hermite
quadrature and moment-matching to fulfill a mutual information-based
acquisition function, which is computationally tractable and efficient. We show
the advantages of our method in both synthetic benchmark datasets and
real-world applications in engineering design.
