A Whittle Index Policy for the Remote Estimation of Multiple Continuous Gauss-Markov Processes over Parallel Channels
A Whittle Index Policy for the Remote Estimation of Multiple Continuous Gauss-Markov Processes over Parallel Channels
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并行通道上多个连续高斯-马尔可夫过程远程估计的 Whittle 指数策略
DOI：
10.1145/3565287.3610263
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Sun, Yin
中科院分区：
文献类型：
--
作者：
Ornee, Tasmeen Zaman;Sun, Yin
在本文中，我们研究了多源远程估计的采样和传输调度问题，其中调度器确定何时从多个连续时间高斯马尔可夫过程中获取样本并将样本通过多个通道发送到远程估计器。样本传输时间在样本和通道之间是独立的。调度器的目标是最小化这些高斯-马尔可夫源的时间平均预期估计误差的加权和。该问题是具有连续状态空间的连续时间多臂老虎机（RMAB）问题。我们证明老虎机是可索引的，并推导出 Whittle 索引的精确表达式。据我们所知，这是第一个用于高斯-马尔可夫过程的多源信号感知远程估计的 Whittle 指数策略。我们进一步研究与信号无关的远程估计，并开发一种 Whittle 指数策略，用于在独立随机传输时间内并行通道上的多源信息时代 (AoI) 最小化。我们的结果结合了远程估计和 AoI 最小化的两个理论框架：基于阈值的采样和基于 Whittle 索引的调度。在单源、单通道场景中，我们证明了采样和调度问题的最优解决方案可以等效地表示为基于阈值的采样策略和基于 Whittle 索引的调度策略。值得注意的是，当且仅当满足两个条件时，Whittle 指数才等于 0：（i）信道空闲，以及（ii）估计误差精确等于基于阈值的采样策略中的阈值。此外，在单源、单通道场景中用于导出基于阈值的采样策略的方法对于在更复杂的多源、多通道场景中建立可索引性和评估 Whittle 指数起着至关重要的作用。我们的数值结果表明，当某些高斯-马尔可夫过程高度不稳定时，所提出的策略比现有策略实现了更高的性能增益。
In this paper, we study a sampling and transmission scheduling problem for multi-source remote estimation, where a scheduler determines when to take samples from multiple continuous-time Gauss-Markov processes and send the samples over multiple channels to remote estimators. The sample transmission times arei.i.d.across samples and channels. The objective of the scheduler is to minimize the weighted sum of the time-average expected estimation errors of these Gauss-Markov sources. This problem is a continuous-time Restless Multi-armed Bandit (RMAB) problem with a continuous state space. We prove that the bandits are indexable and derive an exact expression of the Whittle index. To the extent of our knowledge, this is the first Whittle index policy for multi-source signal-aware remote estimation of Gauss-Markov processes. We further investigate signal-agnostic remote estimation and develop a Whittle index policy for multi-source Age of Information (AoI) minimization over parallel channels withi.i.d.random transmission times. Our results unite two theoretical frameworks for remote estimation and AoI minimization: threshold-based sampling and Whittle index-based scheduling. In the single-source, single-channel scenario, we demonstrate that the optimal solution to the sampling and scheduling problem can be equivalently expressed as both a threshold-based sampling strategy and a Whittle index-based scheduling policy. Notably, the Whittle index is equal to zero if and only if two conditions are satisfied: (i) the channel is idle, and (ii) the estimation error is precisely equal to the threshold in the threshold-based sampling strategy. Moreover, the methodology employed to derive threshold-based sampling strategies in the single-source, single-channel scenario plays a crucial role in establishing indexability and evaluating the Whittle index in the more intricate multi-source, multi-channel scenario. Our numerical results show that the proposed policy achieves high performance gain over the existing policies when some of the Gauss-Markov processes are highly unstable.
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DOI：
10.1017/9781107588981.007
发表时间：
2020
期刊：
Principles of Cyber-Physical Systems
影响因子：
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DOI：
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2016
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DOI：
--
发表时间：
2019
期刊：
International Conference on Complex Information Systems
影响因子：
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J. Nauta;Yara Khaluf;P. Simoens
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DOI：
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发表时间：
2014
期刊：
IEEE Conference on Decision and Control
影响因子：
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