论文标题
通过未知延迟统计的通道进行远程估算的Wiener流程采样
Sampling of the Wiener Process for Remote Estimation over a Channel with Unknown Delay Statistics
论文作者
论文摘要
在本文中，我们研究了Wiener流程的在线抽样问题。目标是在未知的传输延迟分布时，在采样频率约束下将远程估算器的平方误差（MSE）最小化。抽样问题被重新制定为可选的停止问题，我们提出了一种在线抽样算法，可以通过随机近似可以自适应地学习最佳停止阈值。我们证明，累积的MSE遗憾以$ \ MATHCAL {O}（\ ln K）$增长，其中$ k $是样本的数量。通过Le Cam的两个点方法，我们表明，任何在线抽样算法的最糟糕的累积MSE遗憾均由$ω（\ ln K）$降低。因此，提出的在线抽样算法是最小订单最佳的。最后，我们通过数值模拟验证了所提出的算法的性能。
In this paper, we study an online sampling problem of the Wiener process. The goal is to minimize the mean squared error (MSE) of the remote estimator under a sampling frequency constraint when the transmission delay distribution is unknown. The sampling problem is reformulated into an optional stopping problem, and we propose an online sampling algorithm that can adaptively learn the optimal stopping threshold through stochastic approximation. We prove that the cumulative MSE regret grows with rate $\mathcal{O}(\ln k)$, where $k$ is the number of samples. Through Le Cam's two point method, we show that the worst-case cumulative MSE regret of any online sampling algorithm is lower bounded by $Ω(\ln k)$. Hence, the proposed online sampling algorithm is minimax order-optimal. Finally, we validate the performance of the proposed algorithm via numerical simulations.
