One Gradient Frank-Wolfe for Decentralized Online Convex and Submodular Optimization

TL;DR

This paper introduces decentralized online algorithms for convex and DR-submodular optimization, enabling efficient, real-time learning in distributed systems with minimal gradient computations per participant, applicable to federated learning scenarios.

Contribution

It proposes novel decentralized online algorithms for convex and DR-submodular optimization with performance guarantees similar to centralized offline methods, and extends to bandit settings.

Findings

Algorithms achieve comparable performance to centralized offline methods.

Each participant performs only one gradient computation per time step.

Algorithms demonstrate competitive results in real-world experiments.

Abstract

Decentralized learning has been studied intensively in recent years motivated by its wide applications in the context of federated learning. The majority of previous research focuses on the offline setting in which the objective function is static. However, the offline setting becomes unrealistic in numerous machine learning applications that witness the change of massive data. In this paper, we propose \emph{decentralized online} algorithm for convex and continuous DR-submodular optimization, two classes of functions that are present in a variety of machine learning problems. Our algorithms achieve performance guarantees comparable to those in the centralized offline setting. Moreover, on average, each participant performs only a \emph{single} gradient computation per time step. Subsequently, we extend our algorithms to the bandit setting. Finally, we illustrate the competitive performance of our algorithms in real-world experiments.