用数学定理高效定位黑箱分类器边界，节省大量测试成本。
Epsilon-Neighborhood Decision-Boundary Governed Estimation (EDGE) of 2D Black Box Classifier Functions
- 基于中值定理设计采样策略，自动逼近决策边界。
- 在三个测试函数上仅用较少样本达到更优边界估计效果。
- 适合高成本评估场景，如电网稳定性分析等安全关键任务。
准确估计黑箱系统中的决策边界，在保障实际应用中的安全性、质量和可行性方面至关重要。然而，现有方法通过在不确定性区域迭代采样来逐步优化边界估计，既无法保证与真实边界的接近程度，又导致不必要的探索，尤其在评估成本高昂时尤为不利。本文提出ε-邻域决策边界控制估计（EDGE）算法，一种采样高效且不依赖具体函数形式的方法，利用中值定理在用户指定的ε邻域内估计黑箱二分类器的决策边界位置。为验证适用性，研究以含有不确定可再生能源注入的电力系统稳定性问题为例进行了案例分析。在三个测试函数上的评估表明，相比自适应采样和网格搜索，EDGE算法展现出更高的样本效率和更优的边界逼近能力。
原文摘要 · Abstract (English)
Accurately estimating decision boundaries in black box systems is critical when ensuring safety, quality, and feasibility in real-world applications. However, existing methods iteratively refine boundary estimates by sampling in regions of uncertainty, without providing guarantees on the closeness to the decision boundary and also result in unnecessary exploration that is especially disadvantageous when evaluations are costly. This paper presents $\varepsilon$-Neighborhood Decision-Boundary Governed Estimation (EDGE), a sample efficient and function-agnostic algorithm that leverages the intermediate value theorem to estimate the location of the decision boundary of a black box binary classifier within a user-specified $\varepsilon$-neighborhood. To demonstrate applicability, a case study is presented of an electric grid stability problem with uncertain renewable power injection. Evaluations are conducted on three test functions, where it is seen that the EDGE algorithm demonstrates superior sample efficiency and better boundary approximation than adaptive sampling techniques and grid-based searches.
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