Efficient learning by consensus over regular networks

In a network, each agent communicates with its neighbors. All the agents have initial observations, and they update their beliefs with the average of the beliefs in their neighborhoods. It is well known that in the long run, the network will reach consensus. However, the agents do not necessarily converge to the global average of the initial observations of all the agents in the network. Instead, the result is always a weighted average. Moreover, it takes infinite time for the process to converge. In this paper, we address regular networks of agents, where each agent (node) has the same number of agents. We propose a method that allows agents in these networks to learn the global average using the history of its local average in finite time.