Distributed Momentum-Based Frank-Wolfe Algorithm for Stochastic Optimization

This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize global objective function through local computations and information exchanges with neighbors over network. Stochastic optimization problems are usually tackled by variants projected gradient descent. However, projecting point onto feasible set is often expensive. The Frank-Wolfe (FW) method has well-documented merits handling convex constraints, but existing FW algorithms basically developed for centralized settings. In this context, the present work puts forth solver, judiciously combining Nesterov's momentum tracking techniques nonconvex networks. It shown that convergence rate proposed algorithm $\mathcal{O}(k^{-\frac{1}{2}})$ xmlns:xlink="http://www.w3.org/1999/xlink">$\mathcal{O}(1/\log_{2}(k))$ optimization. efficacy demonstrated numerical simulations against competing alternatives.