Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence intervals that are valid uniformly over the growing-into-infinity sample sizes. To address this question, we provide a near-optimal confidence sequence for bounded random variables by utilizing Bentkus' concentration results. We show that it improves on the existing approaches that use the Cram{\'e}r-Chernoff technique such as the Hoeffding, Bernstein, and Bennett inequalities. The resulting confidence sequence is confirmed to be favorable in both synthetic coverage problems and an application to adaptive stopping algorithms.

翻译：许多推论问题,如A/B测试等顺序决定问题,诸如土匪选择等适应性抽样方案,往往是在线性质的。在线推论的根本问题是提供一个对不断增长的至无限抽样规模一致的互信间隔序列。为了解决这一问题,我们通过使用Bentkus的浓度结果,为捆绑随机变量提供了一个近于最佳的互信序列。我们表明,它改进了使用Cram_'e}r-Chernoff技术的现有方法,如Hoffding、Bernstein和Bennett的不平等。由此产生的互信序列在合成覆盖问题和适应性停止算法的应用方面都被证实是有利的。