提出一种新型联邦多目标优化算法，收敛更快更稳定。
A Momentum-Based Variance-Reduced Algorithm for Federated Multiobjective Optimization
- 引入动量驱动梯度估计器降低局部更新方差
- 理论证明收敛速度达到O(T^{-2/3})，优于现有方法
- 适合需要平衡多个目标的联邦学习场景
联邦学习传统上被建模为单目标优化问题，主要关注模型效用最大化。但在实际应用中，机器学习模型常需同时优化多个可能冲突的目标。这催生了联邦多目标优化（FMOO），为联邦学习中联合处理多个任务特定目标提供了自然框架。本文提出一种基于动量的方差缩减算法用于联邦多目标优化。该方法在本地更新中引入动量驱动的梯度估计器，以降低随机更新的方差，从而提升收敛速度。我们建立了理论保证，表明随机选择输出迭代点的期望帕累托平稳度量以O(T^{-2/3})速率衰减，优于现有方法如FSMGDA和FedCMOO的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所提算法的有效性与竞争力。
原文摘要 · Abstract (English)
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.
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