标题： 极小极大设置下的数据高效 quickest 变化检测 显示英文标题

标题： Data-Efficient Quickest Change Detection in Minimax Settings

摘要： 研究了经典的问题即 quickest change detection（快速变化检测），并增加了一个关于检测过程中所用观察成本的约束条件。 将变化点建模为未知常数，并针对该问题提出了 minimax（极小极大）公式。 这些公式的目的是找到停止时间和观察序列的开-关观察控制策略，以最小化最坏情况下可能的平均延迟，同时满足有关错误警报率和变化前观察时间比例的约束条件。 提出了一种称为 DE-CuSum 的算法，并证明了当错误警报率趋于零时，该算法对于所提出的公式渐近最优。 数值结果表明，DE-CuSum 算法具有良好的折中曲线，并且比分数采样方法表现更好，分数采样方法中观测值是通过与观测过程独立的一系列掷硬币的结果跳过的。 这项工作得到了从早期对该问题的贝叶斯版本的研究中获得的见解的指导。 显示英文摘要

摘要： The classical problem of quickest change detection is studied with an additional constraint on the cost of observations used in the detection process. The change point is modeled as an unknown constant, and minimax formulations are proposed for the problem. The objective in these formulations is to find a stopping time and an on-off observation control policy for the observation sequence, to minimize a version of the worst possible average delay, subject to constraints on the false alarm rate and the fraction of time observations are taken before change. An algorithm called DE-CuSum is proposed and is shown to be asymptotically optimal for the proposed formulations, as the false alarm rate goes to zero. Numerical results are used to show that the DE-CuSum algorithm has good trade-off curves and performs significantly better than the approach of fractional sampling, in which the observations are skipped using the outcome of a sequence of coin tosses, independent of the observation process. This work is guided by the insights gained from an earlier study of a Bayesian version of this problem.