研究分布式学习中成对目标的聊天算法，解决传感器网络中的协同优化问题。
On Gossip Algorithms for Machine Learning with Pairwise Objectives
- 设计适用于成对目标函数的聊天算法，支持分布式学习
- 建立收敛性理论框架，给出上界与下界分析
- 适用于相似性学习、排序、聚类等场景
在物联网时代，智能传感器日益普及，但其存储、通信和计算能力有限。由于隐私约束或系统结构限制，如何在分布式网络中共享数据并进行统计学习成为关键挑战。已有大量工作聚焦于基于平均值的目标函数，而本文关注的是具有成对性质的二阶U-统计量形式的目标函数。该设定适用于相似性学习、排序、聚类等实际问题。本文重新审视专为成对目标设计的聊天算法，构建了完整的收敛性理论框架，填补了文献空白。研究明确了算法成功所需的条件，并揭示了图结构特性对其效率的关键影响。特别地，对收敛速度的上下界进行了精细分析。
原文摘要 · Abstract (English)
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.
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