Distributed Detection : Finite-time Analysis and Impact of Network Topology
This addresses the problem of efficient distributed detection for multi-agent systems, offering incremental improvements over asymptotic methods by providing finite-time bounds and network optimization insights.
The paper tackles distributed detection in multi-agent networks by developing an iterative local strategy with finite-time analysis, showing that distributing informative signals to central agents speeds up learning and optimizing weights improves the spectral gap, with bounds expressed in terms of network size, spectral gap, centrality, and signal entropy.
This paper addresses the problem of distributed detection in multi-agent networks. Agents receive private signals about an unknown state of the world. The underlying state is globally identifiable, yet informative signals may be dispersed throughout the network. Using an optimization-based framework, we develop an iterative local strategy for updating individual beliefs. In contrast to the existing literature which focuses on asymptotic learning, we provide a finite-time analysis. Furthermore, we introduce a Kullback-Leibler cost to compare the efficiency of the algorithm to its centralized counterpart. Our bounds on the cost are expressed in terms of network size, spectral gap, centrality of each agent and relative entropy of agents' signal structures. A key observation is that distributing more informative signals to central agents results in a faster learning rate. Furthermore, optimizing the weights, we can speed up learning by improving the spectral gap. We also quantify the effect of link failures on learning speed in symmetric networks. We finally provide numerical simulations which verify our theoretical results.