Nonasymptotic Concentration Rates in Cooperative Learning-Part I: Variational Non-Bayesian Social Learning - Uribe, Cesar A.; Olshevsky, Alexander; Nedic, Angelia (IEEE transactions on control of network systems, 2022)
In this article, we studied the problem of cooperative inference where a group of agents interacts over a network and seeks to estimate a joint parameter that best explains a set of network-wide observationsusing local information only. Agents do not know the network topology or the observations of other agents. We explore a variational interpretation of the Bayesian posterior and its relation to stochastic mirror descent algorithm to prove that, under appropriate assumptions, the beliefs generated by the proposed algorithm concentrate around the true parameter exponentially fast. In part I of this two-part article series, we focus on providing a variational approach to distributed Bayesian filtering. Moreover, we develop computationally efficient algorithms for observation models in exponential families. We provide a novel nonasymptotic belief concentration analysis for distributednon-Bayesian learning on finite hypothesis sets. This new analysis is the basis for the results presented in Part II. We provide the first nonasymptotic belief concentration rate analysis for distributed non-Bayesian learning over networks on compact hypothesis sets in Part II. In addition, we provide extensive numerical analysis for various distributed inference tasks on networks for observational models in the exponential distribution families.