论文标题
基于分布的基于动量的Frank-Wolfe算法，用于随机优化
Distributed Momentum-based Frank-Wolfe Algorithm for Stochastic Optimization
论文作者
论文摘要
本文考虑分布式随机优化，其中许多代理通过本地计算和信息交流通过网络通过本地计算和信息交流来优化全局目标函数。随机优化问题通常由投影随机梯度下降的变体解决。但是，将点投入到可行的套装上通常很昂贵。 Frank-Wolfe（FW）方法在处理凸限制方面具有据可查的优点，但是现有的随机FW算法基本上是针对集中设置开发的。在这种情况下，目前的工作提出了分布式随机的Frank-Wolfe Solver，它是通过明智地结合了Nesterov的动力和梯度跟踪技术，用于随机凸和网络上的非convex优化。结果表明，提出的算法的收敛速率为$ \ MATHCAL {o}（k^{ - \ frac {1} {2}}} $进行凸的优化，而$ \ Mathcal {o}（o}（1/\ Mathrm {logrm {log}} _2（k））$ for nonconve for Nonconvex $ for Nonconvex数值模拟对许多相互竞争的替代方案证明了算法的功效。
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.
