去中心化检测中去中心化的代价研究
On the Price of Decentralization in Decentralized Detection
AI总结：
本文研究去中心化检测中错误概率的极限，揭示了原始社会学习规则因局部权重导致网络不平衡而与集中式存在错误指数差距，并提出改进规则以消除该差距，证明去中心化不造成一阶性能损失。
摘要：
本文研究了一类去中心化检测算法（例如Lalitha等人提出的有向图上的社会学习规则）错误概率的基本极限。在去中心化检测中，节点网络通过局部交换各自观测样本的信息，与邻居共同推断潜在的未知假设。网络中的每个节点对其从邻居处接收到的消息进行加权以形成自己的私有信念，并且只需要知道自身观测的数据生成分布。本文首先证明，虽然Lalitha等人提出的原始社会学习规则在样本数量趋于无穷时能够实现渐近消失的错误概率，但与集中式情形相比，其可达到的错误指数存在差距。这一差距源于网络不平衡，而这种不平衡是由每个节点为加权邻居消息所选择的局部权重引起的。为了弥补这一差距，本文提出了一种改进的学习规则，并证明其能够达到与集中式设置同样大的错误指数。这意味着去中心化在错误概率的指数衰减速率上本质上不会造成一阶惩罚。
英文摘要：
Fundamental limits on the error probabilities of a family of decentralized detection algorithms (eg., the social learning rule proposed by Lalitha et al. over directed graphs are investigated. In decentralized detection, a network of nodes locally exchanging information about the samples they observe with their neighbors to collectively infer the underlying unknown hypothesis. Each node in the network weighs the messages received from its neighbors to form its private belief and only requires knowledge of the data generating distribution of its observation. In this work, it is first shown that while the original social learning rule of Lalitha et al. achieves asymptotically vanishing error probabilities as the number of samples tends to infinity, it suffers a gap in the achievable error exponent compared to the centralized case. The gap is due to the network imbalance caused by the local weights that each node chooses to weigh the messages received from its neighbors. To close this gap, a modified learning rule is proposed and shown to achieve error exponents as large as those in the centralized setup. This implies that there is essentially no first-order penalty caused by decentralization in the exponentially decaying rate of error probabilities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
