On the Effects of Heterogeneous Errors on Multi-fidelity Bayesian
  Optimization
Zahra Zanjani Foumani Amin Yousefpour Mehdi Shishehbor Ramin Bostanabad
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.