论文标题
网络上大型人口游戏的基于信息的加权年龄
Weighted Age of Information based Scheduling for Large Population Games on Networks
论文作者
论文摘要
在本文中，我们考虑了一个离散时间的多代理系统，涉及$ n $成本耦合的网络理性代理，解决共识问题和中央基础站（BS），通过网络安排代理通信。由于对通过网络的传输数量进行了严格的带宽约束，最多最多可以通过网络同时访问其状态信息。在对代理和BS信息结构的标准假设下，我们首先表明代理的控制动作没有任何双重效应，从而可以在每个代理的估计和控制问题之间进行分离。接下来，我们为BS的调度问题提出了一个加权年龄（WAOI）度量，其中权重取决于代理的估计误差。 BS旨在找到最大程度地减少WAOI的最佳调度策略，但要受到硬带宽约束。由于此问题很难，因此我们首先放宽了对软更新率约束的硬性约束，然后通过将其重新定义为马尔可夫决策过程（MDP）来计算放松问题的最佳政策。然后，这激发了带宽约束问题的次优政策，该策略被证明将最佳策略作为$ n \ rightarrow \ infty $。接下来，我们使用均值场游戏框架解决了共识问题，其中我们首先设计了分散的控制策略，以限制$ n $ agen-agent System（如$ n \ rightarrow \ infty $）。通过明确构建平均场系统，我们证明了平均场平衡的存在和独特性。因此，我们表明获得的平衡策略构成了有限代理系统的$ε$ -NASH平衡。最后，我们通过数值模拟验证调度和控制策略的性能。
In this paper, we consider a discrete-time multi-agent system involving $N$ cost-coupled networked rational agents solving a consensus problem and a central Base Station (BS), scheduling agent communications over a network. Due to a hard bandwidth constraint on the number of transmissions through the network, at most $R_d < N$ agents can concurrently access their state information through the network. Under standard assumptions on the information structure of the agents and the BS, we first show that the control actions of the agents are free of any dual effect, allowing for separation between estimation and control problems at each agent. Next, we propose a weighted age of information (WAoI) metric for the scheduling problem of the BS, where the weights depend on the estimation error of the agents. The BS aims to find the optimum scheduling policy that minimizes the WAoI, subject to the hard bandwidth constraint. Since this problem is NP hard, we first relax the hard constraint to a soft update rate constraint, and then compute an optimal policy for the relaxed problem by reformulating it into a Markov Decision Process (MDP). This then inspires a sub-optimal policy for the bandwidth constrained problem, which is shown to approach the optimal policy as $N \rightarrow \infty$. Next, we solve the consensus problem using the mean-field game framework wherein we first design decentralized control policies for a limiting case of the $N$-agent system (as $N \rightarrow \infty$). By explicitly constructing the mean-field system, we prove the existence and uniqueness of the mean-field equilibrium. Consequently, we show that the obtained equilibrium policies constitute an $ε$-Nash equilibrium for the finite agent system. Finally, we validate the performance of both the scheduling and the control policies through numerical simulations.
