Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems

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