Confidence sequences are confidence intervals that can be sequentially tracked, and are valid at arbitrary data-dependent stopping times. This paper presents confidence sequences for a univariate mean of an unknown distribution with a known upper bound on the p-th central moment (p > 1), but allowing for (at most) {\epsilon} fraction of arbitrary distribution corruption, as in Huber's contamination model. We do this by designing new robust exponential supermartingales, and show that the resulting confidence sequences attain the optimal width achieved in the nonsequential setting. Perhaps surprisingly, the constant margin between our sequential result and the lower bound is smaller than even fixed-time robust confidence intervals based on the trimmed mean, for example. Since confidence sequences are a common tool used within A/B/n testing and bandits, these results open the door to sequential experimentation that is robust to outliers and adversarial corruptions.
翻译:信任序列是信任的间隔, 可以按顺序跟踪, 并在任意的数据依赖性停止时有效 。 本文展示了一个未知分布的单亚值的单亚值序列, 在 p- central moment( p > 1) 上方有一个已知的上限( p > 1 ), 但允许任意分配腐败的一小部分, 正如Huber 的污染模式那样 。 我们通过设计新的强势指数性超级组合来做到这一点, 并显示由此产生的信任序列达到了在非顺序环境下达到的最佳宽度 。 也许令人惊讶的是, 我们相继结果和下限之间的恒定比基于刻度平均值的固定时间稳健健的间隔要小得多。 因为信任序列是A/ B/ n 测试和强盗中常用的一种常用的工具, 这些结果打开了连续实验的大门, 从而对外部和对抗性腐败是强大的。