Distributed sequence prediction: A consensus+innovations approach

This paper focuses on the problem of distributed sequence prediction in a network of sparsely interconnected agents, where agents collaborate to achieve provably reasonable predictive performance. An expert assisted online learning algorithm in a distributed setup of the consensus+innovations form is proposed, in which the agents update their weights for the experts' predictions by simultaneously processing the latest network losses (innovations) and the cumulative losses obtained from neighboring agents (consensus). This paper characterizes the regret of the agents' prediction in lieu of the proposed distributed online learning algorithm and establishes the sub-linear regret of the agents' predictions with respect to the best forecasting expert.