Communication-Efficient Distributed Learning Over Networks-Part II: Necessary Conditions for Accuracy

Distributed learning is crucial for many applications such as localization and tracking, autonomy, and crowd sensing. This paper investigates communication-efficient distributed learning of time-varying states over networks. Specifically, the paper considers a network of nodes that infer their current states in a decentralized manner using observations obtained via local sensing and messages obtained via noisy inter-node communications. The paper derives a necessary condition in terms of the sensing and communication capabilities of the network for the boundedness of the learning error over time. The necessary condition is compared with the sufficient condition established in a companion paper and the gap between the two conditions is discussed. The paper provides guidelines for efficient management of the sensing and communication resources for distributed learning in complex networked systems.