Distributed Constrained Optimization with Delayed Subgradient Information over Time-Varying Network under Adaptive Quantization

TL;DR

This paper introduces an adaptive quantization approach for distributed constrained optimization over dynamic networks with delayed subgradient information, achieving optimal convergence rates.

Contribution

It proposes a novel adaptive quantization method integrated with a mirror descent algorithm for distributed optimization with delays and limited communication.

Findings

Achieves optimal convergence rate of O(1/√T).

Effectively handles communication delays and quantization errors.

Demonstrates improved performance through numerical experiments.

Abstract

In this paper, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication channel has a limited data rate. We propose an adaptive quantization method to address this problem. A mirror descent algorithm with delayed subgradient information is established based on the theory of Bregman divergence. With non-Euclidean Bregman projection-based scheme, the proposed method essentially generalizes many previous classical Euclidean projection-based distributed algorithms. Through the proposed adaptive quantization method, the optimal value without any quantization error can be obtained. Furthermore, comprehensive analysis on convergence of the algorithm is carried out and our results show that the optimal convergence rate $O(1/\sqrt{T})$ can be obtained under appropriate conditions. Finally, numerical examples are presented to demonstrate the effectiveness of our algorithm and theoretical results.