A Communication-Efficient Distributed Optimization Algorithm with Coupled Constraints

TL;DR

This paper introduces a communication-efficient distributed optimization algorithm that effectively handles coupled equality constraints using duality theory and differential compression, achieving linear convergence and robust performance.

Contribution

It presents a novel distributed optimization algorithm that combines duality-based reformulation with differential compression to improve communication efficiency and convergence.

Findings

Achieves linear convergence under various compressors

Demonstrates robust performance in numerical experiments

Effectively handles coupled equality constraints

Abstract

This paper designs a communication-efficient distributed optimization algorithm for optimization problems subject to coupled equality constraints. By means of duality theory, the original problem is reformulated to tackle the coupled equality constraints. Furthermore, compressed communication is employed to enhance efficiency whereas introducing compression errors that degrade the performance. To address this, differential compression techniques with dynamic scaling factors are incorporated into the algorithm design. It is shown that the proposed distributed compressed algorithm achieves linear convergence under different compressors. Numerical results further demonstrate its robust performance under different types of compressors while satisfying the equality constraints.