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 the their algorithmic counterparts in the
single-objective federated learning. Our extensive experiments also corroborate
the efficacy of our proposed FMOO algorithms.

提出一种新的联邦多目标学习 (FMOL) 框架，使多个客户端通过分布式和协作的方式解决多目标优化问题，同时保持其训练数据的私密性。该框架支持不同客户端之间的不同目标函数，将多目标优化的思想推广到联邦学习范式中，并提出两种新的联邦多目标优化算法，分别为联邦多梯度下降平均 (FMGDA) 和联邦随机多梯度下降平均 (FSMGDA)。这两种算法通过本地更新显著降低通信成本，并达到与单目标联邦学习的算法相同的收敛速度。大量实验证实了所提出的联邦多目标优化算法的有效性。