Distributed ADMM with Synergetic Communication and Computation

TL;DR

This paper introduces SCCD-ADMM, a distributed optimization algorithm that adaptively balances communication and computation costs by selective neighbor interactions and importance sampling, achieving efficient convergence.

Contribution

The paper presents a novel distributed ADMM algorithm with synergetic communication and computation, including a heuristic neighbor selection and importance sampling, with proven convergence and variance bounds.

Findings

Faster convergence compared to traditional methods.

Reduced communication and computation costs.

Effective in various network topologies.

Abstract

In this paper, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the system. Explicitly, in the proposed algorithm, each node interacts with only part of its neighboring nodes, the number of which is progressively determined according to a heuristic searching procedure, which takes into account both the predicted convergence rate and the communication and computation costs at each iteration, resulting in a trade-off between communication and computation. Then the node chooses its neighboring nodes according to an importance sampling distribution derived theoretically to minimize the variance with the latest information it locally stores. Finally, the node updates its local information with a new update rule which adapts to the number of communication nodes. We prove the convergence of the proposed algorithm and provide an upper bound of the convergence variance brought by randomness. Extensive simulations validate the excellent performances of the proposed algorithm in terms of convergence rate and variance, the overall communication and computation cost, the impact of network topology as well as the time for evaluation, in comparison with the traditional counterparts.