Working Paper: Sequential Parameter Optimization and Optimal Computational Budget Allocation for Noisy Optimization Problems

Sequential parameter optimization (SPO) is a heuristic that combines classical and modern statistical techniques to improve the performance of search algorithms. It includes a broad variety of meta models, e.g., linear models, random forest, and Gaussian process models (Kriging). The selection of an adequate meta model can have significant impact on SPO’s performance. A comparison of different meta models is of great importance. A recent study indicated that random forest based meta models might be a good choice. This rather surprising result will be analyzed in this paper. Moreover, Optimal Computing Budget Allocation (OCBA), which is an enhanced method for handling the computational budget spent for selecting new design points, is presented. The OCBA approach can intelligently determine the most efficient replication numbers. We propose the integration of OCBA into SPO. In this study, SPO is directly used as an optimization method on different noisy mathematical test functions. This is differs from the standard way of using SPO for tuning algorithm parameters in the context of complex real-world applications. Using SPO this way allows for a comparison to other optimization algorithms. Our results reveal that the incorporation of OCBA and the selection of Gaussian process models are highly beneficial. Moreover, SPO outperformed three different alternative optimization algorithms on a set of five noisy mathematical test functions.