  This paper considers distributed stochastic optimization, in which a number
of agents cooperate to optimize a global objective function through local
computations and information exchanges with neighbors over a network.
Stochastic optimization problems are usually tackled by variants of projected
stochastic gradient descent. However, projecting a point onto a feasible set is
often expensive. The Frank-Wolfe (FW) method has well-documented merits in
handling convex constraints, but existing stochastic FW algorithms are
basically developed for centralized settings. In this context, the present work
puts forth a distributed stochastic Frank-Wolfe solver, by judiciously
combining Nesterov's momentum and gradient tracking techniques for stochastic
convex and nonconvex optimization over networks. It is shown that the
convergence rate of the proposed algorithm is $\mathcal{O}(k^{-\frac{1}{2}})$
for convex optimization, and $\mathcal{O}(1/\mathrm{log}_2(k))$ for nonconvex
optimization. The efficacy of the algorithm is demonstrated by numerical
simulations against a number of competing alternatives.
