Quantized Distributed Gradient Tracking Algorithm with Linear Convergence in Directed Networks

TL;DR

This paper introduces a new quantized distributed gradient tracking algorithm that achieves linear convergence over directed networks, significantly improving communication efficiency in distributed optimization.

Contribution

The paper proposes a novel quantized gradient tracking algorithm with explicit quantization level updates, enabling linear convergence with minimal communication bits.

Findings

Q-DGT converges linearly over directed networks.

The algorithm works effectively with just one-bit exchanges.

Numerical results confirm the efficiency and convergence speed.

Abstract

Communication efficiency is a major bottleneck in the applications of distributed networks. To address the problem, the problem of quantized distributed optimization has attracted a lot of attention. However, most of the existing quantized distributed optimization algorithms can only converge sublinearly. To achieve linear convergence, this paper proposes a novel quantized distributed gradient tracking algorithm (Q-DGT) to minimize a finite sum of local objective functions over directed networks. Moreover, we explicitly derive the update rule for the number of quantization levels, and prove that Q-DGT can converge linearly even when the exchanged variables are respectively one bit. Numerical results also confirm the efficiency of the proposed algorithm.