Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimization algorithm that uses inverse distance weighting (IDW) and radial basis functions (RBF) to construct the acquisition function. Rather arbitrary constraints that are simple to evaluate can be easily taken into account. Compared to Bayesian optimization, the proposed algorithm, that we call GLIS (GLobal minimum using Inverse distance weighting and Surrogate radial basis functions), is competitive and computationally lighter, as we show in a set of benchmark global optimization and hyperparameter tuning problems. MATLAB and Python implementations of GLIS are available at http://cse.lab.imtlucca.it/~bemporad/glis.

中文翻译：

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通过逆距离加权和径向基函数进行全局优化

可以通过将替代函数递归拟合到函数样本并最小化获取函数以生成新样本的方法来有效地解决目标函数代价昂贵的全局优化问题。采集步骤在寻找最小替代量的新优化向量（替代量的利用）与寻找可行空间中尚未被访问且可能包含目标函数值更好的区域之间进行权衡（探索）可行空间）。本文提出了一种新的全局优化算法，该算法使用逆距离权重（IDW）和径向基函数（RBF）构造采集函数。相反，可以轻松考虑易于评估的任意约束。与贝叶斯优化相比，我们提出的算法（称为GLIS（使用反距离权重和代理径向基函数的GLobal最小值））具有竞争力，并且计算量更轻，正如我们在一组基准全局优化和超参数调整问题中所展示的那样。GLIS的MA​​TLAB和Python实现可从http://cse.lab.imtlucca.it/~bemporad/glis获得。