The Sample Complexity of Level Set Approximation
Abstract
We study the problem of approximating the level set of an unknown function by sequentially querying its values. We introduce a family of algorithms called Bisect and Approximate through which we reduce the level set approximation problem to a local function approximation problem. We then show how this approach leads to rate-optimal sample complexity guarantees for Hölder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.
Cite
Text
Bachoc et al. "The Sample Complexity of Level Set Approximation." Artificial Intelligence and Statistics, 2021.Markdown
[Bachoc et al. "The Sample Complexity of Level Set Approximation." Artificial Intelligence and Statistics, 2021.](https://mlanthology.org/aistats/2021/bachoc2021aistats-sample/)BibTeX
@inproceedings{bachoc2021aistats-sample,
title = {{The Sample Complexity of Level Set Approximation}},
author = {Bachoc, François and Cesari, Tommaso and Gerchinovitz, Sébastien},
booktitle = {Artificial Intelligence and Statistics},
year = {2021},
pages = {424-432},
volume = {130},
url = {https://mlanthology.org/aistats/2021/bachoc2021aistats-sample/}
}