  We consider distributed optimization over networks where each agent is
associated with a smooth and strongly convex local objective function. We
assume that the agents only have access to unbiased estimators of the gradient
of their objective functions. Motivated by big data applications, our goal lies
in addressing this problem when the dimensionality of the solution space is
possibly large and consequently, the computation of the local gradient mappings
may become expensive. We develop a randomized block-coordinate variant of the
recently developed distributed stochastic gradient tracking (DSGT) method. We
derive non-asymptotic convergence rates of the order $1/k$ and $1/k^2$ in terms
of an optimality metric and a consensus violation metric, respectively.
Importantly, while block-coordinate schemes have been studied for distributed
optimization problems before, the proposed algorithm appears to be the first
randomized block-coordinate gradient tracking method that is equipped with the
aforementioned convergence rate statements. We validate the performance of the
proposed method on the MNIST and a synthetic data set under different network
settings.
