发表机构
Tsinghua University; Shanghai University of Finance and Economics（清华大学; 上海财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对局部差分隐私下顺序分位数推断的难题，提出结合随机化响应与动态链式并行随机梯度下降的在线方法，实现渐近任意时刻有效的置信序列与最佳臂识别。
AI 中文摘要
在局部差分隐私下，顺序分位数推断较为困难，因为每条记录在到达分析者之前都经过随机化，且极限分位数方差依赖于未知密度。我们开发了一种在线程序，将随机化响应与动态链接的并行随机梯度下降（P-SGD）相结合。由此得到的Polyak--Ruppert估计量具有强高斯逼近性质。一个完全由私有迭代计算的跨链二次统计量，能够一致地估计极限方差，而无需单独的在线密度估计器。这些结果产生了渐近置信序列，并在多项式链增长下，实现了渐近时间一致覆盖。臂级构造支持局部私有分位数最佳臂识别、时间一致简单遗憾界以及分位数处理效应的顺序A/B检验。模拟和薪资数据分析展示了所提出方法的有限样本行为及实际应用。
英文摘要
Sequential quantile inference is difficult under local differential privacy because every record is randomized before reaching the analyst and the limiting quantile variance depends on an unknown density. We develop an online procedure that combines randomized response with dynamically chained parallel stochastic gradient descent (P-SGD). The resulting Polyak--Ruppert estimator admits a strong Gaussian approximation. A cross-chain quadratic statistic, computed entirely from private iterates, consistently estimates the limiting variance without a separate online density estimator. These results yield asymptotic confidence sequences and, under polynomial chain growth, asymptotic time-uniform coverage. Arm-wise constructions support locally private quantile best-arm identification, time-uniform simple-regret bounds, and sequential A/B tests of quantile treatment effects. Simulations and salary-data analyses illustrate the finite-sample behavior and practical use of the proposed methods.
