Understanding A Class of Decentralized and Federated Optimization Algorithms: A Multi-Rate Feedback Control Perspective
This provides a novel theoretical framework for researchers in distributed optimization, but it is incremental as it builds on existing algorithms without demonstrating new performance gains.
The paper tackles the problem of understanding and designing distributed optimization algorithms by viewing them through a multi-rate feedback control perspective, showing that many decentralized and federated algorithms can be seen as discretizations of continuous-time control systems, which enables a unified convergence analysis and new algorithm design.
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.