论文标题
较低的置信序列，用于具有有限平均值的非负右重尾观测平均值的变化
A lower confidence sequence for the changing mean of non-negative right heavy-tailed observations with bounded mean
论文作者
论文摘要
置信序列（CS）是任何时间 - 播种顺序推断原始原始序列，它为具有时间均匀覆盖范围保证的可预测参数序列产生适应的集合序列。这项工作构建了一个非参数的非征物较低的CS，用于运行的平均条件期望，其松弛收敛到零，因为非负右重型观测值具有有限的平均值。具体而言，当方差为有限时，方法主导了霍华德等人的经验伯恩斯坦超级马丁莱。 Al。;有了无限的差异，可以适应已知或未知的$（1 +δ）$ - 第矩限制；并且可以使用均匀数量的足够统计数据进行有效近似。在某些情况下，该较低的CS可以转换为闭合间隔CS，其宽度将其宽度转化为零，例如任何有限的实现，或以有限的奖励和无界的重要性权重。参考实现和示例模拟演示了该技术。
A confidence sequence (CS) is an anytime-valid sequential inference primitive which produces an adapted sequence of sets for a predictable parameter sequence with a time-uniform coverage guarantee. This work constructs a non-parametric non-asymptotic lower CS for the running average conditional expectation whose slack converges to zero given non-negative right heavy-tailed observations with bounded mean. Specifically, when the variance is finite the approach dominates the empirical Bernstein supermartingale of Howard et. al.; with infinite variance, can adapt to a known or unknown $(1 + δ)$-th moment bound; and can be efficiently approximated using a sublinear number of sufficient statistics. In certain cases this lower CS can be converted into a closed-interval CS whose width converges to zero, e.g., any bounded realization, or post contextual-bandit inference with bounded rewards and unbounded importance weights. A reference implementation and example simulations demonstrate the technique.
