Distributed Frank-Wolfe Algorithm for Stochastic Aggregative Optimization

This paper is concerned with the distributed stochastic aggregative optimization (DSAO) problem with constraint set, where the local expected-value cost function of each agent depends both on its own decisions and on the aggregation of other agents' decisions, i.e., the aggregation function. For this reason, a distributed aggregative stochastic Frank-Wolfe (DAS-FW) algorithm is designed by introducing the momentum-based variance reduction technique to reduce the variance due to stochastic gradients, introducing the Frank-Wolfe method to deal with constraint. Then, it is theoretically shown that the DAS-FW algorithm owns a sublinear convergence rate of
$O(k^{-\frac{1}{2}})$
for the convex and smooth cost functions. Finally, simulations are presented to verify the validity of our theoretical results.