Comparing Non-Linear Regression Methods on Black-Box Optimization Benchmarks

The paper compares several non-linear regression methods on synthetic data sets generated using standard benchmarks for continuous black-box optimization. For that comparison, we have chosen regression methods that have been used as surrogate models in such optimization: radial basis function networks, Gaussian processes, and random forests. Because the purpose of black-box optimization is frequently some kind of design of experiments, and because a role similar to surrogate models is in the traditional design of experiments played by response surface models, we also include standard response surface models, i.e., polynomial regression. The methods are evaluated based on their mean-squared error and on the Kendall’s rank correlation coefficient between the ordering of function values according to the model and according to the function used to generate the data.