Gradient-push algorithm for distributed optimization with event-triggered communications

TL;DR

This paper introduces a gradient-push algorithm with event-triggered communication for distributed optimization on directed networks, reducing communication costs while ensuring convergence.

Contribution

It proposes a novel event-triggered communication scheme integrated with a gradient-push algorithm for directed networks, with proven convergence guarantees.

Findings

Algorithm effectively reduces communication frequency.

Convergence is established under specific stepsize and threshold conditions.

Numerical experiments confirm the algorithm's efficiency and convergence.

Abstract

Decentralized optimization problems consist of multiple agents connected by a network. The agents have each local cost function, and the goal is to minimize the sum of the functions cooperatively. It requires the agents communicate with each other, and reducing the cost for communication is desired for a communication-limited environment. In this work, we propose a gradient-push algorithm involving event-triggered communication on directed network. Each agent sends its state information to its neighbors only when the difference between the latest sent state and the current state is larger than a threshold. The convergence of the algorithm is established under a decay and a summability condition on a stepsize and a triggering threshold. Numerical experiments are presented to support the effectiveness and the convergence results of the algorithm.