# Decentralized and Parallel Primal and Dual Accelerated Methods for Stochastic Convex Programming Problems

## TL;DR

This paper presents decentralized primal and dual stochastic gradient methods that are optimal in communication steps and can be parallelized at each node, improving efficiency for large-scale convex optimization problems.

## Contribution

It introduces new primal and dual stochastic gradient methods for decentralized convex optimization that are optimal in communication and nearly optimal in oracle calls, with parallelization capabilities.

## Key findings

- Methods are optimal in communication steps.
- Algorithms can be parallelized at each node.
- Applicable to various data science and inverse problems.

## Abstract

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.