AI 中文总结
针对开放客户端-服务器网络中瞬态智能体污染导致朴素平均法无法恢复持久均值的问题，提出两阶段估计框架，通过双层窗口识别与平滑滤波实现均值跟踪，经数值模拟验证有效性。
AI 中文摘要
我们研究开放客户端-服务器网络中的持久智能体识别与均值跟踪问题，其中智能体间歇性参与。该网络由核心的高度规则持久智能体和仅偶尔出现的部分瞬态/非持久智能体组成。由于服务器仅能观测到活跃智能体的二元活动指示器和标量更新，朴素平均法无法恢复活跃持久均值，因为瞬态智能体的更新会污染聚合结果，且异构参与会引入偏差。为解决该问题，我们提出两阶段估计框架：第一阶段，开发基于双层窗口的识别流程：第一层形成单窗口活动决策，第二层跨窗口聚合这些决策，以高概率实现持久智能体与瞬态智能体的分离。在异构伯努利参与下，我们推导了显式有限窗口界，指定服务器需等待多少个窗口才能以高概率实现该分离。第二阶段，利用得到的结构估计，通过平滑滤波器跟踪活跃持久均值，并证明跟踪误差会以几何速率收缩至由目标漂移和滤波器增益决定的邻域。我们提供数值模拟以验证理论结果的有效性。
英文摘要
We study persistent-agent identification and mean tracking in an open client-server network where agents participate intermittently. The network consists of a core of highly regular persistent agents and a subset of transient/non-persistent agents that appear only sporadically. Since the server observes only binary activity indicators and scalar updates from active agents, naive averaging cannot recover the active persistent mean because transient-agent updates contaminate the aggregate, and heterogeneous participation introduces bias. To address this, we propose a two-phase estimation framework. In Phase I, we develop a two-layer window-based identification procedure: the first layer forms single-window activity decisions, while the second aggregates these decisions across windows to create a high-probability separation between persistent and transient agents. Under heterogeneous Bernoulli participation, we derive explicit finite-window bounds that specify how many windows the server must wait for this separation to occur with high probability. In Phase II, we use the resulting structural estimate to track the active persistent mean via a smoothing filter, and show that the tracking error contracts geometrically to a neighborhood determined by the target drift and the filter gain. We provide numerical simulations to illustrate the effectiveness of our theoretical results.
