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arXiv · 2010.13405

The sample complexity of level set approximation

François Bachoc·Tommaso Cesari·Sébastien Gerchinovitz
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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 H{\"o}lder functions, and we investigate how such rates improve when additional smoothness or other structural assumptions hold true.

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François Bachoc, Tommaso Cesari, Sébastien Gerchinovitz. 2020-10-26. The sample complexity of level set approximation. https://arxiv.org/abs/2010.13405

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