We propose a novel nonparametric sequential test for composite hypotheses for means of multiple data streams. Our proposed method, \emph{peeking with expectation-based averaged capital} (PEAK), builds upon the testing-as-betting framework and provides a non-asymptotic $\alpha$-level test across any stopping time. PEAK is computationally tractable and efficiently rejects hypotheses that are incorrect across all potential distributions that satisfy our nonparametric assumption, enabling joint composite hypothesis testing on multiple streams of data. We numerically validate our theoretical findings under the best arm identification and threshold identification in the bandit setting, illustrating both the competitive performance and the computational efficiency of our method against state-of-the-art testing methods.

翻译：我们提出了一种新颖的序贯非参数检验方法，用于多数据流均值的复合假设检验。所提方法——基于期望平均资本的窥探法（PEAK）——建立在"检验即下注"框架之上，可在任意停时提供非渐近的α水平检验。PEAK算法计算便捷，能有效拒绝所有满足非参数假设的潜在分布中不正确的假设，从而实现对多数据流的联合复合假设检验。我们在Bandit场景下的最佳臂识别与阈值识别任务中，通过数值实验验证了理论结果，表明本方法在竞争性能和计算效率方面均优于现有最先进的检验方法。