分散式决策中的一个基本极限
A Fundamental Limit in Decentralized Decision-Making
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中文总结 AI 辅助
本文证明分散式决策存在相对集中式分类的不可约错误概率损失，并推导出与图距离和似然比矩生成函数相关的闭式极限，刻画了不同拓扑下的缩放规律。
中文摘要 AI 辅助
在分散式决策中，多个根据网络图连接的智能体旨在通过收集流式观测数据来解决一个分类问题。由于分散性，它们运行一种迭代算法，在每次迭代中，它们只能与邻居进行局部信息交换。虽然分散式估计解决方案已被证明能够匹配最优集中式系统的性能，但我们在此表明，令人惊讶的是，这一结论并不适用于分散式决策。具体来说，我们证明了最佳分散式决策策略的错误概率相对于最优集中式分类器表现出不可约的损失。这一结果为任何分散式决策策略的性能确立了一个基本极限。我们获得了一个解析关系，表明该极限与分散性和分类之间的相互作用有关。第一个方面通过图中节点之间的距离体现，而第二个方面则通过描述决策问题的似然比的矩生成函数发挥作用。通过将推导出的闭式关系应用于不同的网络拓扑和推理问题，我们观察到一些有趣且可能出乎意料的行为出现。特别是，我们刻画了在常见网络拓扑上损失（随网络规模变化）的缩放规律，表明错误概率可能相差数量级；我们还考察了图中信息丰富与信息贫乏智能体之间的相对距离如何影响性能。
英文摘要
In decentralized decision-making, several agents connected according to a network graph aim at solving a classification problem by collecting streaming observations. Due to decentralization, they run an iterative algorithm where, at each iteration, they can only exchange information locally with their neighbors. While decentralized estimation solutions have been shown to match the performance of optimal centralized systems, we show here that surprisingly this conclusion does not hold for decentralized decision-making. Specifically, we prove that the error probability for the best decentralized decision strategy exhibits an irreducible loss with respect to the optimal centralized classifier. This result establishes a fundamental limit for the performance of any decentralized decision strategy. We obtain an analytical relation showing that this limit is related to the interplay between decentralization and classification. The first aspect appears through the distances between the nodes in the graph, while the second aspect plays through the moment generating functions of the likelihood ratios that describe the decision problem. By applying the derived closed-form relation to different network topologies and inference problems, we observe some interesting and perhaps unexpected behavior emerging. In particular, we characterize the scaling law (with the network size) for the loss over popular network topologies, showing that the error probabilities might differ by orders of magnitude; and we examine how performance is affected by the relative distance between informative and uninformative agents over the graph.
发表机构
- University of Salerno（萨莱诺大学）
- National Inter-University Consortium for Telecommunications (CNIT)（国家大学电信联盟）
机构由 AI 辅助整理，请以论文原文为准。
