A Parameter-free Decentralized Algorithm for Composite Convex Optimization

TL;DR

This paper introduces a decentralized optimization algorithm that adaptively adjusts stepsizes without global information, improving robustness and convergence in composite convex problems over networks.

Contribution

It presents a novel parameter-free decentralized algorithm using local backtracking and a three-operator splitting approach with a new BCV metric for enhanced convergence guarantees.

Findings

Outperforms existing decentralized methods in convergence speed.

Requires no global network information for stepsize adjustment.

Provides robust convergence guarantees for composite convex optimization.

Abstract

The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We propose a decentralized algorithm wherein agents ${\it adaptively}$ adjust their stepsize using local backtracking procedures that require ${\it no}$ ${\it global}$ (network) information or extensive inter-agent communications. Our adaptive decentralized method enjoys robust convergence guarantees, outperforming existing decentralized methods, which are not adaptive. Our design is centered on a three-operator splitting, applied to a reformulation of the optimization problem. This reformulation utilizes a proposed BCV metric, which facilitates decentralized implementation and local stepsize adjustments while guarantying convergence.