DCatalyst: A Unified Accelerated Framework for Decentralized Optimization
Tianyu Cao, Xiaokai Chen, Gesualdo Scutari

TL;DR
DCatalyst is a unified accelerated framework that enhances decentralized optimization algorithms by integrating Nesterov acceleration, achieving optimal complexity and extending acceleration to broader problem classes.
Contribution
It introduces DCatalyst, a novel black-box framework that combines Nesterov acceleration with decentralized algorithms, handling inexact solutions and consensus errors.
Findings
Achieves optimal communication and computational complexity.
Extends acceleration to previously unaccelerated problem classes.
Handles inexact solutions and consensus errors effectively.
Abstract
We study decentralized optimization over a network of agents, modeled as graphs, with no central server. The goal is to minimize , where represents a (strongly) convex function averaging the local agents' losses, and is a convex, extended-value function. We introduce DCatalyst, a unified black-box framework that integrates Nesterov acceleration into decentralized optimization algorithms. %, enhancing their performance. At its core, DCatalyst operates as an \textit{inexact}, \textit{momentum-accelerated} proximal method (forming the outer loop) that seamlessly incorporates any selected decentralized algorithm (as the inner loop). We demonstrate that DCatalyst achieves optimal communication and computational complexity (up to log-factors) across various decentralized algorithms and problem instances. Notably, it extends acceleration capabilities to problem classes…
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Taxonomy
TopicsScheduling and Optimization Algorithms
