High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions

Abstract: Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs, a fundamental problem in many real-world applications. In active learning settings with limited initial data, we aim to iteratively acquire informative points to construct an accurate classifier for this task. In high-dimensional spaces, this becomes challenging where the search volume grows exponentially with increasing dimensionality. We propose TRLSE, an algorithm for high-dimensional LSE, which identifies and refines regions near the threshold boundary with dual acquisition functions operating at both global and local levels. We provide a theoretical analysis of TRLSE's accuracy and show its superior sample efficiency against existing methods through extensive evaluations on multiple synthetic and real-world LSE problems.