Multi-Fidelity Bayesian Optimization via Deep Neural Networks

TL;DR

This paper introduces DNN-MFBO, a deep neural network-based multi-fidelity Bayesian optimization method that captures complex fidelity relationships to improve optimization efficiency and accuracy.

Contribution

The paper presents a novel DNN-MFBO approach that effectively models complex correlations across fidelities, enhancing objective estimation and optimization performance.

Findings

Outperforms existing methods on synthetic benchmarks

Effective in real-world engineering design applications

Captures complex fidelity relationships efficiently

Abstract

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.