  Bayesian optimization (BO) is a powerful paradigm for derivative-free global
optimization of a black-box objective function (BOF) that is expensive to
evaluate. However, the overhead of BO can still be prohibitive for problems
with highly expensive function evaluations. In this paper, we investigate how
to reduce the required number of function evaluations for BO without compromise
in solution quality. We explore the idea of posterior regularization to harness
low fidelity (LF) data within the Gaussian process upper confidence bound
(GP-UCB) framework. The LF data can arise from previous evaluations of an LF
approximation of the BOF or of a related optimization task. An extra GP model
called LF-GP is trained to fit the LF data. We develop an operator termed
dynamic weighted product of experts (DW-POE) fusion. The regularization is
induced by this operator on the posterior of the BOF. The impact of the LF GP
model on the resulting regularized posterior is adaptively adjusted via
Bayesian formalism. Extensive experimental results on benchmark BOF
optimization tasks demonstrate the superior performance of the proposed
algorithm over state-of-the-art.
