Comparison of Decentralized and Centralized Update Paradigms for Distributed Remote Estimation

In this work, we perform a comparative study of centralized and decentralized update strategies for the basic remote tracking problem of many distributed users/devices with randomly evolving states. Our goal is to reveal the impact of the fundamentally different tradeoffs that exist between information accuracy and communication cost under these two update paradigms. In one extreme, decentralized updates are triggered by distributed users/transmitters based on exact local state-information, but also at a higher cost due to the need for uncoordinated multi-user communication. In the other extreme, centralized updates are triggered by the common tracker/receiver based on estimated global state-information, but also at a lower cost due to the capability of coordinated multi-user communication. We use a generic superlinear function to model the communication cost with respect to the number of simultaneous updates for multiple sources. We characterize the conditions under which transmitter-driven decentralized update policies outperform their receiver-driven centralized counterparts for symmetric sources, and vice versa. Further, we extend the results to a scenario where system parameters are unknown and develop learning-based update policies that asymptotically achieve the minimum cost levels attained by the optimal policies.