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.

翻译：我们通过按顺序查询一个未知函数的值来研究近似于该值的问题。 我们引入了一套算法, 叫做“ 比昆特和近似 ”, 以此将设定的近似问题降低到本地函数近似问题 。 然后我们展示这个方法如何导致为 H =“ o}lder ” 函数提供最优的样本复杂度保障, 我们调查在额外的平滑性或其他结构性假设都属实时, 此类比率会如何改善 。