High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions
This work addresses a fundamental problem in active learning for real-world applications, though it appears incremental as it builds on existing methods with specific improvements.
The paper tackles the challenge of level set estimation in high-dimensional spaces by proposing TRLSE, an algorithm that uses trust regions and dual acquisition functions to efficiently classify inputs based on an unknown function's threshold, achieving superior sample efficiency in evaluations.
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.