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In this paper we present an optimization-based view of distributed parameterestimation and observational social learning in networks. Agents receive asequence of random, independent and identically distributed (i.i.d.) signals,each of which individually may not be informative about the underlying truestate, but the signals together are globally informative enough to make thetrue state identifiable. Using an optimization-based characterization ofBayesian learning as proximal stochastic gradient descent (withKullback-Leibler divergence from a prior as a proximal function), we show howto efficiently use a distributed, online variant of Nesterov's dual averagingmethod to solve the estimation with purely local information. When the truestate is globally identifiable, and the network is connected, we prove thatagents eventually learn the true parameter using a randomized gossip scheme. Wedemonstrate that with high probability the convergence is exponentially fastwith a rate dependent on the KL divergence of observations under the true statefrom observations under the second likeliest state. Furthermore, our work alsohighlights the possibility of learning under continuous adaptation of networkwhich is a consequence of employing constant, unit stepsize for the algorithm.

Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging