We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique, we show that the proposed methods with stochastic oracle can be additionally parallelized at each node. The considered algorithms can be applied to many data science problems and inverse problems.

中文翻译：

---

随机凸规划问题的分散和并行原始和双加速方法

我们为分散的凸优化问题引入了原始和对偶随机梯度预言机方法。对于原始预言机和双重预言机，所提出的方法在通信步骤的数量方面都是最佳的。然而，对于目标的所有类别，每个节点的预言机调用数量的最优性只发生在对数因子和平滑度的概念上。通过使用小批量技术，我们表明所提出的随机预言方法可以在每个节点上额外并行化。所考虑的算法可以应用于许多数据科学问题和逆问题。