Batch Sequential Adaptive Designs for Global Optimization

Abstract

Compared with the fixed-run designs, the sequential adaptive designs (SAD) are thought to be more efficient and effective. Efficient global optimization (EGO) is one of the most popular SAD methods for expensive black-box optimization problems. A well-recognized weakness of the original EGO in complex computer experiments is that it is serial, and hence the modern parallel computing techniques cannot be utilized to speed up the running of simulator experiments. For those multiple points EGO methods, the heavy computation and points clustering are the obstacles. In this work, a novel batch SAD method, named "accelerated EGO", is forwarded by using a refined sampling/importance resampling (SIR) method to search the points with large expected improvement (EI) values. The computation burden of the new method is much lighter, and the points clustering is also avoided. The efficiency of the proposed SAD is validated by nine classic test functions with dimension from 2 to 12. The empirical results show that the proposed algorithm indeed can parallelize original EGO, and gain much improvement compared against the other parallel EGO algorithm especially under high-dimensional case. Additionally, we also apply the new method to the hyper-parameter tuning of Support Vector Machine (SVM). Accelerated EGO obtains comparable cross validation accuracy with other methods and the CPU time can be reduced a lot due to the parallel computation and sampling method.