  In this paper, we study the problem of distributed multi-agent optimization
over a network, where each agent possesses a local cost function that is smooth
and strongly convex. The global objective is to find a common solution that
minimizes the average of all cost functions. Assuming agents only have access
to unbiased estimates of the gradients of their local cost functions, we
consider a distributed stochastic gradient tracking method. We show that, in
expectation, the iterates generated by each agent are attracted to a
neighborhood of the optimal solution, where they accumulate exponentially fast
(under a constant step size choice). More importantly, the limiting (expected)
error bounds on the distance of the iterates from the optimal solution decrease
with the network size, which is a comparable performance to a centralized
stochastic gradient algorithm. Numerical examples further demonstrate the
effectiveness of the method.
