Improvement-Based Acquisition Functions for Level Set Estimation

Identifying regions where a function lies above or below a threshold is of significant interest to the scientific community. Estimating function values relative to a threshold is often framed in an active learning setting as a classification problem. Probabilistic models like Gaussian Processes (GPs) are often used to model the underlying function, and utility functions are used to infer the true class at the evaluation point. In this work, we introduce expected improvement-level set estimation (EI-LSE) and probability of improvement-level set estimation (PI-LSE), natural extensions of popular Bayesian optimization acquisition functions, to level set estimation (LSE). Besides providing theoretical guarantees on the misclassification rate, we evaluate these methods on synthetic and real-world datasets and compare them with other state-of-the-art LSE algorithms.