On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian Optimization
This work addresses a bottleneck in MFBO for applications like materials design by making it more robust to heterogeneous errors, though it is incremental as it builds on existing MFBO methods.
The paper tackles the problem of multi-fidelity Bayesian optimization (MFBO) under unrealistic assumptions about low-fidelity data correlation and noise, proposing a method that learns separate noise models and handles locally correlated sources, resulting in improved performance as demonstrated in analytical examples and materials design engineering problems.
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.