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 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非参数序贯检验方法，用于对多数据流的均值进行复合假设检验。所提出的方法——基于期望平均资本的窥探（PEAK）——建立在“以测试为赌注”框架之上，并能在任意停止时间提供非渐近的α水平检验。PEAK计算上易处理，并能高效拒绝所有满足我们非参数假设的潜在分布中不成立的假设，从而实现对多数据流的联合复合假设检验。我们在赌博机设定下的最优臂识别和阈值识别中，数值验证了我们的理论结果，表明我们方法在计算效率上优于当前最先进的检验方法。