Client selection significantly affects the system convergence efficiency and is a crucial problem in federated learning. Existing methods often select clients by evaluating each round individually and overlook the necessity for long-term optimization, resulting in suboptimal performance and potential fairness issues. In this study, we propose a novel client selection strategy designed to emulate the performance achieved with full client participation. In a single round, we select clients by minimizing the gradient-space estimation error between the client subset and the full client set. In multi-round selection, we introduce a novel individual fairness constraint, which ensures that clients with similar data distributions have similar frequencies of being selected. This constraint guides the client selection process from a long-term perspective. We employ Lyapunov optimization and submodular functions to efficiently identify the optimal subset of clients, and provide a theoretical analysis of the convergence ability. Experiments demonstrate that the proposed strategy significantly improves both accuracy and fairness compared to previous methods while also exhibiting efficiency by incurring minimal time overhead.

翻译：客户端选择显著影响系统收敛效率，是联邦学习中的关键问题。现有方法通常通过逐轮独立评估来选择客户端，忽视了长期优化的必要性，导致性能欠佳并可能引发公平性问题。本研究提出一种新颖的客户端选择策略，旨在模拟全客户端参与所能达到的性能。在单轮选择中，我们通过最小化客户端子集与全体客户端集之间的梯度空间估计误差来选择客户端。在多轮选择中，我们引入了一种创新的个体公平性约束，确保具有相似数据分布的客户端具有相近的被选频率。该约束从长期视角指导客户端选择过程。我们采用李雅普诺夫优化与次模函数高效识别最优客户端子集，并提供收敛能力的理论分析。实验表明，相较于现有方法，所提策略在准确性与公平性方面均取得显著提升，同时因引入极小的时间开销而展现出优异的效率。