An Exact Quantized Decentralized Gradient Descent Algorithm

TL;DR

This paper introduces QDGD, a novel decentralized optimization algorithm that achieves vanishing consensus error despite quantization noise, effectively addressing communication bottlenecks in distributed systems.

Contribution

The paper presents the first algorithm capable of vanishing consensus error under quantization noise in decentralized optimization.

Findings

QDGD achieves vanishing mean solution error.

Theoretical convergence rate matches simulation results.

Addresses communication bottleneck in distributed optimization.

Abstract

We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local information. We prove that under standard strong convexity and smoothness assumptions for the objective function, QDGD achieves a vanishing mean solution error under customary conditions for quantizers. To the best of our knowledge, this is the first algorithm that achieves vanishing consensus error in the presence of quantization noise. Moreover, we provide simulation results that show tight agreement between our derived theoretical convergence rate and the numerical results.