Identifying the top-$k$ items is fundamental but often prohibitive when exact valuations are expensive. We study a two-oracle setting with a fast, noisy weak oracle and a scarce, high-fidelity strong oracle (e.g., human expert verification or expensive simulation). We first analyze a simple screen-then-certify baseline (STC) and prove it makes at most $m(4\varepsilon_{\max})$ strong calls given jointly valid weak confidence intervals with maximum radius $\varepsilon_{\max}$, where $m(\cdot)$ denotes the near-tie mass around the top-$k$ threshold. We establish a conditional lower bound of $Ω(m(\varepsilon_{\max}))$ for any algorithm given the same weak uncertainty. Our main contribution is ACE, an adaptive certification algorithm that focuses strong queries on critical boundary items, achieving the same $O(m(4\varepsilon_{\max}))$ bound while reducing strong calls in practice. We then introduce ACE-W, a fully adaptive two-phase method that allocates weak budget adaptively before running ACE, further reducing strong costs.

翻译：识别前$k$个最优项是基础性问题，但当精确估值成本高昂时往往难以实现。本文研究一种双预言机场景：一个快速但含噪声的弱预言机，以及一个稀缺但高保真的强预言机（例如人类专家验证或昂贵的仿真）。我们首先分析一种简单的"筛选-认证"基线方法（STC），并证明在给定最大半径为$\varepsilon_{\max}$的联合有效弱置信区间时，该方法最多进行$m(4\varepsilon_{\max})$次强预言机调用，其中$m(\cdot)$表示前$k$阈值附近的近似平局质量。针对相同弱不确定性条件，我们建立了任意算法的条件性下界$\Omega(m(\varepsilon_{\max}))$。本文的核心贡献是ACE算法——一种将强查询聚焦于关键边界项的自适应认证算法，在保持$O(m(4\varepsilon_{\max}))$理论界的同时，实践中显著减少了强预言机调用次数。进一步提出ACE-W方法，这种完全自适应的两阶段算法在运行ACE前自适应分配弱查询预算，从而进一步降低强预言机调用成本。