Title: Distributed Learning for Cooperative Inference,
Abstract: We study the problem of cooperative inference where a group of agents
interact over a network and seek to estimate a joint parameter that best
explains a set of observations. Agents do not know the network topology or the
observations of other agents. We explore a variational interpretation of the
Bayesian posterior density, and its relation to the stochastic mirror descent
algorithm, to propose a new distributed learning algorithm. We show that, under
appropriate assumptions, the beliefs generated by the proposed algorithm
concentrate around the true parameter exponentially fast. We provide explicit
non-asymptotic bounds for the convergence rate. Moreover, we develop explicit
and computationally efficient algorithms for observation models belonging to
exponential families.