发表机构
College of Mathematics and Statistics, Chongqing Jiaotong University; School of Science, RMIT University; School of Mathematics, Yunnan Normal University（重庆交通大学数学与统计学院; 皇家墨尔本理工大学理学院; 云南师范大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对联邦多目标优化问题，提出融入动量驱动梯度估计器的方差缩减算法，其收敛速率优于现有方法，经基准实验验证有效。
AI 中文摘要
传统联邦学习被形式化为单目标优化问题，主要聚焦于最大化模型效用。然而在实际应用中，机器学习模型往往需要同时优化多个可能相互冲突的目标，这催生了联邦多目标优化（FMOO），它为联合处理联邦学习中多个特定任务目标提供了自然框架。本文提出一种基于动量的联邦多目标优化方差缩减算法，该方法在本地更新中融入动量驱动的梯度估计器以降低随机更新的方差，从而提升收敛速率。我们建立了理论保证，表明随机选取的输出迭代的期望帕累托平稳性度量以$\boldsymbol{\textit{O}}(T^{-2/3})$的速率衰减，优于现有方法如FSMGDA和FedCMOO所达到的$\boldsymbol{\textit{O}}(T^{-1/2})$速率。在联邦多目标优化基准上的数值实验验证了该算法的有效性和竞争力。
英文摘要
Federated learning has traditionally been formulated as a single-objective optimization problem, primarily focused on maximizing model utility. In real-world applications, however, machine learning models often need to optimize multiple and potentially conflicting objectives simultaneously. This motivates federated multiobjective optimization (FMOO), which provides a natural framework for jointly handling multiple task-specific objectives in federated learning. In this paper, we propose a momentum-based variance-reduced algorithm for federated multiobjective optimization. The method incorporates a momentum-driven gradient estimator into the local updates to reduce the variance of stochastic updates, leading to an improved convergence rate. We establish theoretical guarantees showing that the expected Pareto stationarity measure of a randomly selected output iterate decays at a rate of $\mathcal{O}(T^{-2/3})$, improving upon the $\mathcal{O}(T^{-1/2})$ rates established for existing methods such as FSMGDA and FedCMOO. Numerical experiments on federated multiobjective optimization benchmarks demonstrate the effectiveness and competitive performance of the proposed algorithm.
