Multi-Fidelity Bayesian Optimization via Deep Neural Networks
This addresses the challenge of reducing optimization costs in black-box function optimization for applications like engineering design, though it appears incremental as it builds on existing multi-fidelity BO methods.
The paper tackles the problem of inefficient multi-fidelity Bayesian optimization by proposing DNN-MFBO, which captures complex correlations across fidelities to improve objective function estimation, showing advantages in synthetic benchmarks and real-world engineering design applications.
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.