A radial basis function method for noisy global optimisation
提出一种新的响应面方法，用于优化昂贵且含噪的黑箱目标函数，基于Gutmann的RBF方法，使用正则化最小二乘准则构建近似并确定新样本点，提供了收敛性证明和数值示例。
We present a novel response surface method for global optimisation of an expensive and noisy (black-box) objective function, where error bounds on the deviation of the observed noisy function values from their true counterparts are available. The method is based on Gutmann's well-established RBF method for minimising an expensive and deterministic objective function, which has become popular both from a theoretical and practical perspective. To construct suitable radial basis function approximants to the objective function and to determine new sample points for successive evaluation of the expensive noisy objective, the method uses a regularised least-squares criterion. In particular, new points are defined by means of a target value, analogous to the original RBF method. We provide essential convergence results, and provide a numerical illustration of the method by means of a simple test problem.