Extremum information transfer over networks for remote estimation and distributed learning

Most modern large-scale multi-agent systems operate by taking actions based on local data and cooperate by exchanging information over communication networks. Due to the abundance of sensors, each agent is capable of generating more data than what could be supported by communication channels in near real-time. Thus, not every piece of information can be transmitted perfectly over the network. Such communication constraints lead to a large number of challenging research problems, some of which have been solved, and many more that remain open. The focus of this paper is to present a comprehensive treatment of this new class of fundamental problems in information dissemination over networks, which is based on the notion of extremum information . The unifying theme herein is that the strategic communication, i.e., when the agents decide on what to transmit based on their observed data (or state), leads to the optimality of extremum (or outlier) information. In other words, when a random information source deviates from the average by a certain amount, that realization should be prioritized for transmission. This creates a natural ranking of the data points based on their magnitude such that if an agent has access to more than one piece of information, the ones that display the largest deviation from the average are transmitted and the rest is discarded. We show that the problem of finding the top- K largest measurements over a network can be cast and efficiently implemented as a distributed inference problem. Curiously, the same principle holds for the framework of distributed optimization, leading to a class of state-dependent protocols known as max-dissent. While still a heuristic, max-dissent can considerably accelerate the convergence to an optimal solution in distributed convex optimization. We provide open problems and present several directions for future work including questions related to cyber-security and robustness of such networks as well as new architectures for distributed learning and optimization.