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.

翻译：在现实应用中，确保安全性、质量和可行性时，准确估计黑盒系统的决策边界至关重要。然而，现有方法通过在不确定区域采样来迭代优化边界估计，既无法保证与决策边界的接近程度，又会导致不必要的探索，这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），这是一种样本高效且与函数无关的算法，利用介值定理来估计黑盒二元分类器决策边界的位置，且保证位于用户指定的ε邻域内。为展示其适用性，本文以具有不确定可再生能源注入的电网稳定性问题为例进行案例研究。在三个测试函数上的评估表明，与自适应采样技术和基于网格的搜索方法相比，EDGE算法展现出更优的样本效率和更好的边界逼近能力。