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）作为支撑多智能体多任务学习应用的基础性问题而备受关注。然而，现有MOO文献中的算法仍局限于集中式学习场景，无法满足此类多智能体多任务学习应用中分布式特性与数据隐私需求。为此，我们提出了一种新型联邦多目标学习（FMOL）框架，该框架允许多个客户端在保持训练数据私密性的同时，分布式协作求解MOO问题。值得注意的是，本框架允许不同客户端采用差异化目标函数集以支持广泛的应用场景，这首次将MOO公式推广至联邦学习范式。针对该FMOL框架，我们提出了两种新型联邦多目标优化（FMOO）算法：联邦多梯度下降平均算法（FMGDA）与联邦随机多梯度下降平均算法（FSMGDA）。两种算法均允许本地更新以显著降低通信成本，同时实现与单目标联邦学习中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。