  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.
