  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.
