Limited Communications Distributed Optimization via Deep Unfolded Distributed ADMM

TL;DR

This paper introduces a deep unfolding approach for D-ADMM, enabling efficient distributed optimization with significantly fewer messages exchanged, while maintaining performance and interpretability.

Contribution

It proposes unfolded D-ADMM, a novel method that uses deep unfolding to reduce communication in distributed optimization without sacrificing effectiveness.

Findings

Reduces communication cost dramatically compared to standard D-ADMM.

Maintains high performance in distributed estimation and learning tasks.

Operates effectively with a fixed, small number of messages exchanged.

Abstract

Distributed optimization is a fundamental framework for collaborative inference and decision making in decentralized multi-agent systems. The operation is modeled as the joint minimization of a shared objective which typically depends on observations gathered locally by each agent. Distributed optimization algorithms, such as the common D-ADMM, tackle this task by iteratively combining local computations and message exchanges. One of the main challenges associated with distributed optimization, and particularly with D-ADMM, is that it requires a large number of communications, i.e., messages exchanged between the agents, to reach consensus. This can make D-ADMM costly in power, latency, and channel resources. In this work we propose unfolded D-ADMM, which follows the emerging deep unfolding methodology to enable D-ADMM to operate reliably with a predefined and small number of messages exchanged by each agent. Unfolded D-ADMM fully preserves the operation of D-ADMM, while leveraging data to tune the hyperparameters of each iteration of the algorithm. These hyperparameters can either be agent-specific, aiming at achieving the best performance within a fixed number of iterations over a given network, or shared among the agents, allowing to learn to distributedly optimize over different networks. For both settings, our unfolded D-ADMM operates with limited communications, while preserving the interpretability and flexibility of the original D-ADMM algorithm. We specialize unfolded D-ADMM for two representative settings: a distributed estimation task, considering a sparse recovery setup, and a distributed learning scenario, where multiple agents collaborate in learning a machine learning model. Our numerical results demonstrate that the proposed approach dramatically reduces the number of communications utilized by D-ADMM, without compromising on its performance.