On Gossip Algorithms for Machine Learning with Pairwise Objectives

2026-03-25

AI Summary

This work addresses the challenge of optimizing pairwise objective functions—such as those arising in U-statistics—in distributed Internet-of-Things systems, where conventional gossip algorithms designed for average-based objectives are ill-suited for tasks like similarity learning, ranking, and clustering. The paper proposes a novel gossip algorithm tailored to pairwise objectives and establishes, for the first time, a rigorous theoretical framework for its convergence. It derives tight upper and lower bounds on the convergence rate and elucidates the critical influence of the underlying network graph topology on algorithmic efficiency. By filling a key theoretical gap in the distributed optimization of U-statistics, this study provides a solid foundation for deploying privacy-sensitive or communication-constrained distributed machine learning applications.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

In the IoT era, information is more and more frequently picked up by connected smart sensors with increasing, though limited, storage, communication and computation abilities. Whether due to privacy constraints or to the structure of the distributed system, the development of statistical learning methods dedicated to data that are shared over a network is now a major issue. Gossip-based algorithms have been developed for the purpose of solving a wide variety of statistical learning tasks, ranging from data aggregation over sensor networks to decentralized multi-agent optimization. Whereas the vast majority of contributions consider situations where the function to be estimated or optimized is a basic average of individual observations, it is the goal of this article to investigate the case where the latter is of pairwise nature, taking the form of a U -statistic of degree two. Motivated by various problems such as similarity learning, ranking or clustering for instance, we revisit gossip algorithms specifically designed for pairwise objective functions and provide a comprehensive theoretical framework for their convergence. This analysis fills a gap in the literature by establishing conditions under which these methods succeed, and by identifying the graph properties that critically affect their efficiency. In particular, a refined analysis of the convergence upper and lower bounds is performed.

Problem

• gossip algorithms
• pairwise objectives
• U-statistics
• distributed learning
• sensor networks

Innovation

• gossip algorithms
• pairwise objectives
• U-statistics
• decentralized optimization
• convergence analysis