Batch sequential adaptive designs for global optimization

Abstract

Efficient global optimization (EGO) is one of the most popular sequential adaptive design (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 batch 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, the new method is applied to the hyper-parameter tuning of support vector machine (SVM) and XGBoost models in machine learning. 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.

Appendix

The constant Liar (CL), one of the parallel EGO algorithms, is a sequential strategy for targeting the multiple points at each cycle, in which the surrogate model is updated (still without hyper-parameter re-estimation) at each iteration with a value $L\in R$ exogenously fixed by the user, called a “lie”. Three values, $\min \{\varvec{y}\}$, $\max \{\varvec{y}\}$ and $\text {mean}\{\varvec{y}\}$ were considered in Ginsbourger et al. (2010). In our simulations, the lie “L” is taken as $\min \{\varvec{y}\}$.