# Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation

arXiv: https://arxiv.org/abs/2203.09751 · HTML: https://mlsanity.com/paper/2203.09751/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 70 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 14 of 14)

- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Max-value Entropy Search for Efficient Bayesian Optimization](https://mlsanity.com/paper/1703.01968/) (2017)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [Efficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees](https://mlsanity.com/paper/2006.15779/) (2020)
- [Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation](https://mlsanity.com/paper/1610.07379/) (2016)
- [GLASSES: Relieving The Myopia Of Bayesian Optimisation](https://mlsanity.com/paper/1510.06299/) (2015)
- [BINOCULARS for Efficient, Nonmyopic Sequential Experimental Design](https://mlsanity.com/paper/1909.04568/) (2019)
- [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)
- [Correcting boundary over-exploration deficiencies in Bayesian optimization with virtual derivative sign observations](https://mlsanity.com/paper/1704.00963/) (2017)
- [Adaptive Design of Experiments for Conservative Estimation of Excursion Sets](https://mlsanity.com/paper/1611.07256/) (2016)
- [Evaluating Gaussian Process Metamodels and Sequential Designs for Noisy Level Set Estimation](https://mlsanity.com/paper/1807.06712/) (2018)
- [Adaptive Nonparametric Psychophysics](https://mlsanity.com/paper/2104.09549/) (2021)

## Built on by (most cited first, 6 of 6)

- [Active Learning for Level Set Estimation Using Randomized Straddle Algorithms](https://mlsanity.com/paper/2408.03144/) (2024)
- [Mixed Likelihood Variational Gaussian Processes](https://mlsanity.com/paper/2503.04138/) (2025)
- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)
- [Response Time Improves Choice Prediction and Function Estimation for Gaussian Process Models of Perception and Preferences](https://mlsanity.com/paper/2306.06296/) (2023)
- [An (ε,δ)-accurate level set estimation with a stopping criterion](https://mlsanity.com/paper/2503.20272/) (2025)
- [Dose-finding design based on level set estimation in phase I cancer clinical trials](https://mlsanity.com/paper/2504.09157/) (2025)

## Abstract (arXiv)

Level set estimation (LSE) is the problem of identifying regions where an unknown function takes values above or below a specified threshold. Active sampling strategies for efficient LSE have primarily been studied in continuous-valued functions. Motivated by applications in human psychophysics where common experimental designs produce binary responses, we study LSE active sampling with Bernoulli outcomes. With Gaussian process classification surrogate models, the look-ahead model posteriors used by state-of-the-art continuous-output methods are intractable. However, we derive analytic expressions for look-ahead posteriors of sublevel set membership, and show how these lead to analytic expressions for a class of look-ahead LSE acquisition functions, including information-based methods. Benchmark experiments show the importance of considering the global look-ahead impact on the entire posterior. We demonstrate a clear benefit to using this new class of acquisition functions on benchmark problems, and on a challenging real-world task of estimating a high-dimensional contrast sensitivity function.