社区共识：尽管存在敌手和异构连通性仍能局部收敛
Community Consensus: Converging Locally despite Adversaries and Heterogeneous Connectivity
AI总结：
研究存在恶意智能体和异构连通性的网络，提出社区共识概念，放宽全局共识条件，证明局部子集仍能收敛到相同值。
摘要：
我们引入了社区共识的概念，即在存在恶意智能体的情况下使用一种著名的基于中位数的共识算法。我们考虑具有多个连接良好的区域（我们称之为社区）的网络，这些区域具有特定的鲁棒性和最小度属性。先前的工作推导了在网络中实现全局共识的必要和充分属性条件。然而，这要求网络图的最小度与网络中恶意智能体的数量成正比，这在大型网络中不太实际。在本研究中，我们对先前的结果进行了自然的推广。我们刻画了这样的情况：尽管未达到全局共识，某些智能体子集 $V_i$ 仍会在彼此之间收敛到相同的值 $M_i$。为了达成这种新型共识，我们定义了更为宽松的要求，涉及每个社区中恶意智能体的数量，以及连接社区内智能体与社区外智能体的边数 $k$。
英文摘要：
We introduce the concept of community consensus in the presence of malicious agents using a well-known median-based consensus algorithm. We consider networks that have multiple well-connected regions that we term communities, characterized by specific robustness and minimum degree properties. Prior work derives conditions on properties that are necessary and sufficient for achieving global consensus in a network. This, however, requires the minimum degree of the network graph to be proportional to the number of malicious agents in the network, which is not very practical in large networks. In this work, we present a natural generalization of this previous result. We characterize cases where, although global consensus is not reached, some subsets of agents $V_i$ will still converge to the same values $M_i$ among themselves. To reach this new type of consensus, we define more relaxed requirements in terms of the number of malicious agents in each community, and the number $k$ of edges connecting an agent in a community to agents external to the community.
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