On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian Optimization

TL;DR

This paper introduces a multi-fidelity Bayesian optimization method that models source-specific noise and handles locally correlated low-fidelity data, improving optimization efficiency in practical, costly experimental settings.

Contribution

It proposes a novel MF emulation approach that relaxes common assumptions, enabling effective use of biased and locally correlated low-fidelity sources in Bayesian optimization.

Findings

Improved optimization performance with locally correlated LF data.

Effective noise modeling for each data source.

Validated on materials design problems.

Abstract

Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the fused data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we dispense with these incorrect assumptions by proposing an MF emulation method that (1) learns a noise model for each data source, and (2) enables MFBO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.