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

• URL: http://arxiv.org/abs/2602.12391v1
• Date: Thu, 12 Feb 2026 20:36:04 GMT
• Title: High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functions
• Authors: Giang Ngo, Dat Phan Trong, Dang Nguyen, Sunil Gupta,
• Abstract summary: Level set estimation (LSE) classifies whether an unknown function's value exceeds a specified threshold for given inputs.<n>We propose TRLSE, an algorithm for high-dimensional LSE, which identifies and refines regions near the threshold boundary.<n>We show its superior sample efficiency against existing methods through extensive evaluations on multiple synthetic and real-world LSE problems.
• Score: 10.577125986583432
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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