This paper introduces range regularization for federated learning with linear systematic components to enhance statistical accuracy and induce cross-client regularity conducive to quantization, coding, and resource efficiency. Our approach identifies features with shared weights across different clients and adaptively clusters the weights of personalized features at extreme values, a process we refer to as polar clustering. Theoretical analysis of the associated estimators poses significant challenges due to the seminorm nature and non-decomposability of the regularizer. We develop new proof techniques for the nonasymptotic analysis of statistical accuracy and faithful pattern recovery. Moreover, a fast optimization algorithm that leverages varying degrees of local strong convexity is proposed to reduce iteration complexity. Experiments support the efficacy and efficiency of the proposed approach.

翻译：本文针对具备线性系统组件的联邦学习引入范围正则化，旨在提升统计精度并促进跨客户端的正则性，从而利于量化、编码及资源效率优化。该方法识别不同客户端间权重共享的特征，并自适应地将个性化特征的权重聚类至极值，我们将此过程称为极值聚类。由于正则化项的半范数性质与不可分解性，对其相关估计量进行理论分析面临显著挑战。我们开发了用于统计精度与可靠模式恢复的非渐近分析的新证明技术。此外，提出了一种利用局部强凸性差异度的快速优化算法，以降低迭代复杂度。实验验证了所提方法的有效性与高效性。