论文标题
微型批次随机三 - 操作员分裂以进行分布式优化
Mini-batch stochastic three-operator splitting for distributed optimization
论文作者
论文摘要
我们考虑一个代理网络，每个网络都有其自身的私人成本，包括两个可能的非平滑凸功能，其中一个由线性操作员组成。在每次迭代中，每个代理都执行本地计算，并且只能与邻居进行通信。我们研究的挑战性方面是，私人成本功能的平滑部分是作为期望值，而代理只能通过重尾随机甲骨文来访问问题的这一部分。为了解决此类基于抽样的优化问题，我们提出了三角形预处理的原始二重算法的随机扩展。我们证明了该方案的几乎确定收敛性，并通过数值实验验证了该方法的性能。
We consider a network of agents, each with its own private cost consisting of a sum of two possibly nonsmooth convex functions, one of which is composed with a linear operator. At every iteration each agent performs local calculations and can only communicate with its neighbors. The challenging aspect of our study is that the smooth part of the private cost function is given as an expected value and agents only have access to this part of the problem formulation via a heavy-tailed stochastic oracle. To tackle such sampling-based optimization problems, we propose a stochastic extension of the triangular pre-conditioned primal-dual algorithm. We demonstrate almost sure convergence of the scheme and validate the performance of the method via numerical experiments.
