Sequential estimation of distributed parameters in networks

The problem of estimating a set of unknown parameters in a multi-agent network is considered. Each agent can make noisy observations from a subset of the unknown parameters, and different agents can potentially observe common parameters. The objective of each agent is to estimate its observed unknown parameters. This paper focuses on sequentially estimating the parameters such that, in the quickest fashion, all the agents form reliable estimates for their designated parameters. A proper estimation cost function is adopted in order to signify the fidelity of the estimates to the ground truth, and to ensure consistency in the estimates of different agents. By imposing practical constraints on the number of data points that the network affords to process, the sequential strategy dynamically decides about the minimum number of measurements required to form reliable estimates, the agents from which these measurements should be collected, and the optimal estimators for each agent. Specifically, a sequential strategy is proposed, which consists of the stopping rule of the sampling process, a data-adaptive control policy for selecting the agents over time, and a set of estimators, combination of which admits asymptotic optimality.