A Decentralized Primal-Dual Framework for Non-convex Smooth Consensus Optimization

TL;DR

This paper introduces ADAPD, a decentralized primal-dual algorithmic framework for non-convex smooth consensus optimization, achieving optimal communication complexity and demonstrating superior performance in numerical experiments.

Contribution

The paper proposes a novel ADAPD framework with flexible variants for non-convex consensus optimization, combining inexact local solves and neighbor communication for improved efficiency.

Findings

Achieves theoretically optimal communication complexity.

Demonstrates superior performance over existing decentralized methods.

Effective in deep-learning applications.

Abstract

In this work, we introduce ADAPD, $\textbf{A}$ $\textbf{D}$ecentr$\textbf{A}$lized $\textbf{P}$rimal-$\textbf{D}$ual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. The proposed framework relies on a novel problem formulation that elicits ADMM-type updates, where each agent first inexactly solves a local strongly convex subproblem with any method of its choice and then performs a neighbor communication to update a set of dual variables. We present two variants that allow for a single gradient step for the primal updates or multiple communications for the dual updates, to exploit the tradeoff between the per-iteration cost and the number of iterations. When multiple communications are performed, ADAPD can achieve theoretically optimal communication complexity results for non-convex and smooth consensus problems. Numerical experiments on several applications, including a deep-learning one, demonstrate the superiority of ADAPD over several popularly used decentralized methods.