# Distributed Nesterov gradient methods over arbitrary graphs

## TL;DR

This paper introduces a novel distributed Nesterov gradient method that operates over arbitrary graphs without requiring doubly-stochastic weights, achieving accelerated convergence compared to existing methods.

## Contribution

The paper proposes the BN method that works with row- and column-stochastic weights, and a FROZEN variant that only needs row-stochastic weights, broadening applicability.

## Key findings

- Achieves acceleration over state-of-the-art distributed optimization methods.
- Works on arbitrary strongly-connected graphs without doubly-stochastic weights.
- FROZEN variant reduces communication requirements at the cost of extra iterations.

## Abstract

In this letter, we introduce a distributed Nesterov method, termed as $\mathcal{ABN}$, that does not require doubly-stochastic weight matrices. Instead, the implementation is based on a simultaneous application of both row- and column-stochastic weights that makes this method applicable to arbitrary (strongly-connected) graphs. Since constructing column-stochastic weights needs additional information (the number of outgoing neighbors at each agent), not available in certain communication protocols, we derive a variation, termed as FROZEN, that only requires row-stochastic weights but at the expense of additional iterations for eigenvector learning. We numerically study these algorithms for various objective functions and network parameters and show that the proposed distributed Nesterov methods achieve acceleration compared to the current state-of-the-art methods for distributed optimization.