We study active learning (AL) based on gaussian processes (GPs) for efficiently enumerating all of the local minimum solutions of a black-box function. This problem is challenging because local solutions are characterized by their zero gradient and positive-definite Hessian properties, but those derivatives cannot be directly observed. We propose a new AL method in which the input points are sequentially selected such that the confidence intervals of the GP derivatives are effectively updated for enumerating local minimum solutions. We theoretically analyze the proposed method and demonstrate its usefulness through numerical experiments.

中文翻译：

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基于高斯过程导数的枚举局部极小值的主动学习

我们研究了基于高斯过程 (GP) 的主动学习 (AL)，以有效枚举黑盒函数的所有局部最小解。这个问题具有挑战性，因为局部解的特征在于它们的零梯度和正定 Hessian 特性，但这些导数不能直接观察到。我们提出了一种新的 AL 方法，其中依次选择输入点，从而有效地更新 GP 导数的置信区间以枚举局部最小解。我们从理论上分析了所提出的方法，并通过数值实验证明了其有效性。