摘要
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 O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.
基金
supported in part by the National Key R&D Program of China(2021YFB1714800)
the National Natural Science Foundation of China(62222303,62073035,62173034,61925303,62088101,61873033)
the CAAI-Huawei MindSpore Open Fund
the Chongqing Natural Science Foundation(2021ZX4100027)。