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In the last decade, considerable advances have been made in reliability-based design optimization (RBDO). One assumption in RBDO is that the complete information of input uncertainties are known. However, this assumption is not valid in practical engineering applications, due to the lack of sufficient data. In practical engineering design, information concerning uncertainty parameters is usually in the form of finite samples. Existing methods in uncertainty based design optimization cannot handle design problems involving epistemic uncertainty with a shortage of information. Recently, a novel method referred to as Bayesian Reliability-Based Design Optimization (BRBDO) was proposed to properly handle design problems when engaging both epistemic and aleatory uncertainties [1]. However, when a design problem involves a large number of epistemic variables, the computation task for BRBDO becomes extremely expensive.