# Stochastic Bregman Parallel Direction Method of Multipliers for Distributed Optimization

## TL;DR

This paper introduces a stochastic variant of the Bregman parallel direction method of multipliers for distributed optimization, reducing computational load and enabling larger network applications while maintaining convergence guarantees.

## Contribution

It generalizes BPDMM to a stochastic setting with convergence proofs, facilitating scalable distributed optimization in multi-agent systems.

## Key findings

- Achieves global convergence of stochastic BPDMM.
- Establishes an O(1/T) iteration complexity.
- Demonstrates effectiveness through numerical examples.

## Abstract

Bregman parallel direction method of multipliers (BPDMM) efficiently solves distributed optimization over a network, which arises in a wide spectrum of collaborative multi-agent learning applications. In this paper, we generalize BPDMM to stochastic BPDMM, where each iteration only solves local optimization on a randomly selected subset of nodes rather than all the nodes in the network. Such generalization reduce the need for computational resources and allows applications to larger scale networks. We establish both the global convergence and the \(O(1/T)\) iteration complexity of stochastic BPDMM. We demonstrate our results via numerical examples.