  In this paper we consider convergence rate problems for stochastic
strongly-convex optimization in the non-Euclidean sense with a constraint set
over a time-varying multi-agent network. We propose two efficient non-Euclidean
stochastic subgradient descent algorithms based on the Bregman divergence as
distance-measuring function rather than the Euclidean distances that were
employed by the standard distributed stochastic projected subgradient
algorithms. For distributed optimization of nonsmooth and strongly convex
functions whose only stochastic subgradients are available, the first algorithm
recovers the best previous known rate of O(ln(T)/T) (where T is the total
number of iterations). The second algorithm is an epoch variant of the first
algorithm that attains the optimal convergence rate of O(1/T), matching that of
the best previously known centralized stochastic subgradient algorithm.
Finally, we report some simulation results to illustrate the proposed
algorithms.
