We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student-t observations; (ii) Student-t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

我们考虑学习有噪声的黑盒功能超过给定阈值的水平集的问题。为了有效地重建水平集，我们研究了高斯过程（GP）元模型。我们的重点是高度随机的模拟器，尤其是具有重尾的模拟噪声和低信噪比的模拟器。为了防止噪声规格错误，我们评估了三种变体的性能：（i）具有Student- t观测值的GP ；（ⅱ）以学生吨流程（TP）；（iii）对响应信号进行建模的分类GP。结合这些元模型，我们分析了一些采集函数，以指导顺序实验设计，将现有的逐步不确定性降低标准扩展到随机轮廓寻找上下文。这也激发了我们（近似）更新公式的开发，以有效地计算此类获取函数。我们的方案通过在1-6维上使用各种综合实验进行基准测试。我们还考虑了水平集估计在确定百慕大期权在财务中的最优行使政策中的应用。