Dynamic decision-making in rapidly evolving research domains, including marketing, finance, and pharmaceutical development, presents a significant challenge. Researchers frequently confront the need for real-time action within a doubly sequential framework characterized by the continuous influx of high-volume data streams and the intermittent arrival of novel tasks. This calls for the development and implementation of new online inference protocols capable of handling both the continuous processing of incoming information and the efficient allocation of resources to address emerging priorities. We introduce a novel class of Safe and Always-Valid Alpha-investing (SAVA) rules that leverages powerful tools including always valid p-values, e-processes, and online false discovery rate methods. The SAVA algorithm effectively integrates information across all tasks, mitigates the alpha-death problem, and controls the false selection rate (FSR) at all decision points. We validate the efficacy of the SAVA framework through rigorous theoretical analysis and extensive numerical experiments. Our results demonstrate that SAVA not only offers effective control of the FSR but also significantly improves statistical power compared to traditional online testing approaches.

翻译：在快速演进的研究领域（如市场营销、金融和药物研发）中，动态决策面临重大挑战。研究者常需在双重序贯框架下实时行动，该框架以持续涌入的高容量数据流和间歇性新任务到达为特征。这要求开发并实施新型在线推断协议，能够同时处理连续输入信息流并高效分配资源以应对新出现的优先任务。本文提出一类新颖的安全且始终有效的Alpha投资（SAVA）规则，其利用了始终有效的p值、e过程及在线错误发现率方法等强大工具。SAVA算法有效整合所有任务信息，缓解alpha衰减问题，并在所有决策点控制错误选择率（FSR）。通过严格的理论分析和大量数值实验，我们验证了SAVA框架的有效性。结果表明，与传统在线检验方法相比，SAVA不仅能有效控制FSR，还显著提升了统计功效。