Distributed and Inexact Proximal Gradient Method for Online Convex Optimization

Abstract

This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution.

To be presented at the European Control Conference 2021 (ECC'21)

References in corpus (7)

• Distributed Algorithms for Composite Optimization: Unified Framework and Convergence Analysis
• Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Node Error
• Can Primal Methods Outperform Primal-dual Methods in Decentralized Dynamic Optimization?
• An Asynchronous Distributed Proximal Gradient Method for Composite Convex Optimization
• Distributed Online Convex Optimization with Improved Dynamic Regret
• A Prediction-Correction Algorithm for Real-Time Model Predictive Control
• Principled Analyses and Design of First-Order Methods with Inexact Proximal Operators

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