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# The Sample Complexity of Level Set Approximation

*Proceedings of The 24th International Conference on Artificial Intelligence and Statistics*, PMLR 130:424-432, 2021.

#### 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.