Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective

TL;DR

This paper offers a novel control-theoretic framework to analyze and design a broad class of decentralized and federated optimization algorithms, enhancing understanding and enabling new algorithm development.

Contribution

It introduces a multi-rate feedback control perspective that unifies and analyzes various distributed algorithms, providing a generic convergence framework and new design insights.

Findings

Unified analysis of decentralized algorithms via control theory

Development of a generic convergence framework

Design of new algorithms using the proposed framework

Abstract

Distributed algorithms have been playing an increasingly important role in many applications such as machine learning, signal processing, and control. Significant research efforts have been devoted to developing and analyzing new algorithms for various applications. In this work, we provide a fresh perspective to understand, analyze, and design distributed optimization algorithms. Through the lens of multi-rate feedback control, we show that a wide class of distributed algorithms, including popular decentralized/federated schemes, can be viewed as discretizing a certain continuous-time feedback control system, possibly with multiple sampling rates, such as decentralized gradient descent, gradient tracking, and federated averaging. This key observation not only allows us to develop a generic framework to analyze the convergence of the entire algorithm class. More importantly, it also leads to an interesting way of designing new distributed algorithms. We develop the theory behind our framework and provide examples to highlight how the framework can be used in practice.