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Bayesian optimization (BO) is a powerful paradigm for derivative-free globaloptimization of a black-box objective function (BOF) that is expensive toevaluate. However, the overhead of BO can still be prohibitive for problemswith highly expensive function evaluations. In this paper, we investigate howto reduce the required number of function evaluations for BO without compromisein solution quality. We explore the idea of posterior regularization to harnesslow fidelity (LF) data within the Gaussian process upper confidence bound(GP-UCB) framework. The LF data can arise from previous evaluations of an LFapproximation of the BOF or of a related optimization task. An extra GP modelcalled LF-GP is trained to fit the LF data. We develop an operator termeddynamic weighted product of experts (DW-POE) fusion. The regularization isinduced by this operator on the posterior of the BOF. The impact of the LF GPmodel on the resulting regularized posterior is adaptively adjusted viaBayesian formalism. Extensive experimental results on benchmark BOFoptimization tasks demonstrate the superior performance of the proposedalgorithm over state-of-the-art.

Harnessing Low-Fidelity Data to Accelerate Bayesian Optimization via Posterior Regularization