  This paper proposes a distributed stochastic projection-free algorithm for
large-scale constrained finite-sum optimization whose constraint set is
complicated such that the projection onto the constraint set can be expensive.
The global cost function is allocated to multiple agents, each of which
computes its local stochastic gradients and communicates with its neighbors to
solve the global problem. Stochastic gradient methods enable low computational
cost, while they are hard and slow to converge due to the variance caused by
random sampling. To construct a convergent distributed stochastic
projection-free algorithm, this paper incorporates a variance reduction
technique and gradient tracking technique in the Frank-Wolfe update. We develop
a sampling rule for the variance reduction technique to reduce the variance
introduced by stochastic gradients. Complete and rigorous proofs show that the
proposed distributed projection-free algorithm converges with a sublinear
convergence rate and enjoys superior complexity guarantees for both convex and
non-convex objective functions. By comparative simulations, we demonstrate the
convergence and computational efficiency of the proposed algorithm.
