In recent years, multi-objective optimization (MOO) emerges as a foundational problem underpinning many multi-agent multi-task learning applications. However, existing algorithms in MOO literature remain limited to centralized learning settings, which do not satisfy the distributed nature and data privacy needs of such multi-agent multi-task learning applications. This motivates us to propose a new federated multi-objective learning (FMOL) framework with multiple clients distributively and collaboratively solving an MOO problem while keeping their training data private. Notably, our FMOL framework allows a different set of objective functions across different clients to support a wide range of applications, which advances and generalizes the MOO formulation to the federated learning paradigm for the first time. For this FMOL framework, we propose two new federated multi-objective optimization (FMOO) algorithms called federated multi-gradient descent averaging (FMGDA) and federated stochastic multi-gradient descent averaging (FSMGDA). Both algorithms allow local updates to significantly reduce communication costs, while achieving the {\em same} convergence rates as those of their algorithmic counterparts in the single-objective federated learning. Our extensive experiments also corroborate the efficacy of our proposed FMOO algorithms.

翻译：近年来，多目标优化（MOO）作为支撑众多多智能体多任务学习应用的基础问题而出现。然而，现有MOO文献中的算法仍局限于集中式学习场景，无法满足这类多智能体多任务学习应用的分布式特性与数据隐私需求。为此，我们提出了一种新的联邦多目标学习（FMOL）框架，该框架允许多个客户端在保持各自训练数据隐私的前提下，分布式协同求解MOO问题。值得注意的是，我们的FMOL框架支持不同客户端设置不同的目标函数集合，从而适用于广泛的应用场景，这首次将MOO形式推广并泛化至联邦学习范式。针对该FMOL框架，我们提出了两种新的联邦多目标优化（FMOO）算法：联邦多梯度下降平均法（FMGDA）和联邦随机多梯度下降平均法（FSMGDA）。这两种算法均允许通过局部更新显著降低通信开销，同时保持与单目标联邦学习对应算法相同的收敛速率。大量实验也验证了我们所提出的FMOO算法的有效性。