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：置信序列是可顺序追踪的置信区间，在任意依赖数据的停止时间均有效。本文针对具有已知$p$阶中心矩上界（$p>1$）的未知分布的单变量均值，提出允许（至多）$\epsilon$比例任意分布污染的置信序列，正如Huber污染模型所述。我们通过设计新型鲁棒指数超鞅实现这一目标，并证明所得置信序列达到非序贯设置下的最优宽度。令人惊讶的是，与基于截尾均值的固定时间鲁棒置信区间相比，我们序列结果与下界之间的常数差距甚至更小。由于置信序列常被用于A/B/n测试和bandit算法，这些结果为对异常值和对抗性污染具有鲁棒性的序贯实验开辟了道路。