In large-scale hypothesis testing, computing exact $p$-values or $e$-values is often resource-intensive, creating a need for budget-aware inferential methods. We propose a general framework for active hypothesis testing that leverages inexpensive auxiliary statistics to allocate a global computational budget. For each hypothesis, our data-adaptive procedure probabilistically decides whether to compute the exact test statistic or a transformed proxy, guaranteeing a valid $p$-value or $e$-value while satisfying the exact budget constraint. Theoretical guarantees are established for our constructions, showing that the procedure achieves optimality for $e$-values and for $p$-values under independence, and admissibility for $p$-values under general dependence. Empirical results from simulations and two real-world applications, including a large-scale genome-wide association study (GWAS) and a clinical prediction task leveraging large language models (LLM), demonstrate that our framework improves statistical efficiency under fixed resource limits.

翻译：在大规模假设检验中，精确计算$p$值或$e$值通常需要大量资源，因此需要预算感知的推断方法。我们提出了一种主动假设检验的通用框架，该框架利用廉价的辅助统计量来分配全局计算预算。对于每个假设，我们的数据自适应程序以概率方式决定是计算精确检验统计量还是转换后的代理统计量，从而在满足精确预算约束的同时保证有效的$p$值或$e$值。我们为所提方法建立了理论保证，表明该程序在独立条件下对$e$值和$p$值均达到最优性，且在一般相依条件下对$p$值具有可采纳性。来自模拟实验和两个实际应用（包括大规模全基因组关联研究（GWAS）和利用大语言模型（LLM）的临床预测任务）的实证结果表明，我们的框架在固定资源限制下提高了统计效率。