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

arXiv: https://arxiv.org/abs/2602.12391 · HTML: https://mlsanity.com/paper/2602.12391/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 12 Feb 2026.

## Builds on (most cited first, 18 of 18)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Bayesian Optimization in a Billion Dimensions via Random Embeddings](https://mlsanity.com/paper/1301.1942/) (2013)
- [High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces](https://mlsanity.com/paper/2103.00349/) (2021)
- [Vanilla Bayesian Optimization Performs Great in High Dimensions](https://mlsanity.com/paper/2402.02229/) (2024)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [BOCK : Bayesian Optimization with Cylindrical Kernels](https://mlsanity.com/paper/1806.01619/) (2018)
- [High-Dimensional Bayesian Optimization via Additive Models with Overlapping Groups](https://mlsanity.com/paper/1802.07028/) (2018)
- [Increasing the Scope as You Learn: Adaptive Bayesian Optimization in Nested Subspaces](https://mlsanity.com/paper/2304.11468/) (2023)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [High-Dimensional Bayesian Optimization via Tree-Structured Additive Models](https://mlsanity.com/paper/2012.13088/) (2020)
- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Robust Super-Level Set Estimation using Gaussian Processes](https://mlsanity.com/paper/1811.09977/) (2018)
- [An Information-Theoretic Framework for Unifying Active Learning Problems](https://mlsanity.com/paper/2012.10695/) (2020)
- [Multiscale Gaussian Process Level Set Estimation](https://mlsanity.com/paper/1902.09682/) (2019)
- [High Dimensional Level Set Estimation with Bayesian Neural Network](https://mlsanity.com/paper/2012.09973/) (2020)
- [Active Level Set Estimation for Continuous Search Space with Theoretical Guarantee](https://mlsanity.com/paper/2402.16237/) (2024)
- [Robust Transfer Learning for Active Level Set Estimation with Locally Adaptive Gaussian Process Prior](https://mlsanity.com/paper/2410.05660/) (2024)

## Built on by (most cited first, 1 of 1)

- [ATLAS-AL: Adaptive Trust-Region for Latent Adversarial Searches via Active Learning](https://mlsanity.com/paper/2610.07323/) (2026)

## Abstract (arXiv)

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.