# Asynchronous Gradient-Push

## TL;DR

This paper introduces Asynchronous Gradient-Push, an algorithm for distributed optimization in multi-agent networks that operates asynchronously, converges to the global minimum under certain conditions, and outperforms synchronous methods in speed and robustness.

## Contribution

The paper presents a novel asynchronous algorithm for distributed convex optimization that guarantees convergence and improves efficiency over existing synchronous approaches.

## Key findings

- Converges to a neighborhood of the global minimum depending on asynchrony.
- Achieves exact global minimizer when agents work at the same rate.
- Outperforms state-of-the-art synchronous methods in speed and robustness.

## Abstract

We consider a multi-agent framework for distributed optimization where each agent has access to a local smooth strongly convex function, and the collective goal is to achieve consensus on the parameters that minimize the sum of the agents' local functions. We propose an algorithm wherein each agent operates asynchronously and independently of the other agents. When the local functions are strongly-convex with Lipschitz-continuous gradients, we show that the iterates at each agent converge to a neighborhood of the global minimum, where the neighborhood size depends on the degree of asynchrony in the multi-agent network. When the agents work at the same rate, convergence to the global minimizer is achieved. Numerical experiments demonstrate that Asynchronous Gradient-Push can minimize the global objective faster than state-of-the-art synchronous first-order methods, is more robust to failing or stalling agents, and scales better with the network size.