Robust Super-Level Set Estimation Using Gaussian Processes
Abstract
This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that function evaluations are costly. To select the next query point, we propose maximizing the expected volume of the domain identified as above the threshold as predicted by a Gaussian process, robustified by a variance term. We also give asymptotic guarantees on the exploration effect of the algorithm, regardless of the prior misspecification. We show by various numerical examples that our approach also outperforms existing techniques in the literature in practice.
Cite
Text
Zanette et al. "Robust Super-Level Set Estimation Using Gaussian Processes." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2018. doi:10.1007/978-3-030-10928-8_17Markdown
[Zanette et al. "Robust Super-Level Set Estimation Using Gaussian Processes." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2018.](https://mlanthology.org/ecmlpkdd/2018/zanette2018ecmlpkdd-robust/) doi:10.1007/978-3-030-10928-8_17BibTeX
@inproceedings{zanette2018ecmlpkdd-robust,
title = {{Robust Super-Level Set Estimation Using Gaussian Processes}},
author = {Zanette, Andrea and Zhang, Junzi and Kochenderfer, Mykel J.},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2018},
pages = {276-291},
doi = {10.1007/978-3-030-10928-8_17},
url = {https://mlanthology.org/ecmlpkdd/2018/zanette2018ecmlpkdd-robust/}
}