Distributed Prediction-Correction ADMM for Time-Varying Convex Optimization

TL;DR

This paper presents a dual-regularized ADMM algorithm for distributed, time-varying convex optimization that predicts future costs to improve convergence and outperforms some existing methods.

Contribution

It introduces a novel prediction-correction framework with dual regularization for improved convergence in time-varying distributed optimization.

Findings

The algorithm guarantees linear convergence.

It outperforms inexact gradient-based methods in asymptotic error.

It reduces consensus constraint violation in time-varying scenarios.

Abstract

This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on past observations, and exploit this information to solve the time-varying problem more effectively. In order to guarantee linear convergence of the algorithm, a regularization is applied to the dual, yielding a dual-regularized ADMM. We analyze the convergence properties of the time-varying algorithm, as well as the regularization error of the dual-regularized ADMM. Numerical results show that in time-varying settings, despite the regularization error, the performance of the dual-regularized ADMM can outperform inexact gradient-based methods, as well as exact dual decomposition techniques, in terms of asymptotical error and consensus constraint violation.