We consider a distributed learning setup where a network of agents
sequentially access realizations of a set of random variables with unknown
distributions. The network objective is to find a parametrized distribution
that best describes their joint observations in the sense of the
Kullback-Leibler divergence. Apart from recent efforts in the literature, we
analyze the case of countably many hypotheses and the case of a continuum of
hypotheses. We provide non-asymptotic bounds for the concentration rate of the
agents' beliefs around the correct hypothesis in terms of the number of agents,
the network parameters, and the learning abilities of the agents. Additionally,
we provide a novel motivation for a general set of distributed Non-Bayesian
update rules as instances of the distributed stochastic mirror descent
algorithm.Comment: Submitted to CDC201