An important question that often arises in the operation of networked systems is whether to collect the real-time data or to estimate them based on the previously collected data. Various factors should be taken into account such as how informative the data are at each time instant for state estimation, how costly and credible the collected data are, and how rapidly the data vary with time. The above question can be formulated as a dynamic decision making problem with imperfect information structure, where a decision maker wishes to find an efficient way to switch between data collection and data estimation while the quality of the estimation depends on the previously collected data (i.e., duality effect). In this paper, the evolution of the state of each node is modeled as an exchangeable Markov process for discrete features and equivariant linear system for continuous features, where the data of interest are defined in the former case as the empirical distribution of the states, and in the latter case as the weighted average of the states. When the data are collected, they may or may not be credible, according to a Bernoulli distribution. Based on a novel planning space, a Bellman equation is proposed to identify a near-optimal strategy whose computational complexity is logarithmic with respect to the inverse of the desired maximum distance from the optimal solution, and polynomial with respect to the number of nodes. A reinforcement learning algorithm is developed for the case when the model is not known exactly, and its convergence to the near-optimal solution is shown subsequently. In addition, a certainty threshold is introduced that determines when data estimation is more desirable than data collection, as the number of nodes increases. For the special case of linear dynamics, a separation principle is constructed wherein the optimal estimate is computed by a Kalman-like filter, irrespective of the probability distribution of random variables. It is shown that the complexity of finding the proposed sampling strategy, in this special case, is independent of the size of the state space and the number of nodes. Examples of a sensor network, a communication network and a social network are provided.

中文翻译：

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数据收集与数据估计：动态网络中的基本权衡


网络系统运行中经常出现的一个重要问题是收集实时数据还是根据先前收集的数据来估计它们。应考虑各种因素，例如用于状态估计的每个时刻的数据的信息量有多大，收集的数据的成本和可信度如何，以及数据随时间变化的速度有多快。上述问题可以表述为一个信息结构不完善的动态决策问题，其中决策者希望找到一种有效的方式在数据收集和数据估计之间切换，而估计的质量取决于先前收集的数据（即，对偶效应）。本文将每个节点的状态演化建模为离散特征的可交换马尔可夫过程和连续特征的等变线性系统，其中，在前一种情况下，感兴趣的数据被定义为状态的经验分布，并且在后一种情况下为各州的加权平均值。根据伯努利分布，收集数据后，它们可能可信，也可能不可信。基于新颖的规划空间，提出了贝尔曼方程来识别近乎最优的策略，其计算复杂度相对于与最优解的期望最大距离的倒数而言是对数，并且相对于节点数量而言是多项式。针对模型未知的情况开发了强化学习算法，随后显示了其收敛到接近最优解的情况。此外，还引入了确定性阈值，用于确定随着节点数量的增加，数据估计何时比数据收集更可取。 对于线性动力学的特殊情况，构建了分离原理，其中通过类卡尔曼滤波器计算最佳估计，而不考虑随机变量的概率分布。结果表明，在这种特殊情况下，找到所提出的采样策略的复杂性与状态空间的大小和节点的数量无关。提供了传感器网络、通信网络和社交网络的示例。