联邦学习团队终于有了一个兼顾理论严谨和实际效率的正则化方案——极值聚类能显著提升模型压缩和通信效率，做分布式系统或资源受限场景的开发者可以直接参考实验设置。
本文提出了一种名为“范围正则化”的新方法，用于联邦学习场景，旨在提升统计精度并促进跨客户端的规律性，从而有利于量化、编码和资源效率。该方法通过识别不同客户端间共享权重的特征，并将个性化特征的权重自适应地聚类到极值（称为极值聚类），解决了传统正则化器因半范数特性和不可分解性带来的理论分析难题。研究者开发了新的非渐近分析技术，用于评估统计精度和模式恢复的可靠性，并提出了利用局部强凸性的快速优化算法以减少迭代复杂度。实验验证了该方法在联邦学习中的有效性和效率，为分布式机器学习提供了新的理论工具。
Range Penalization: Theoretical Insights with Applications in Federated Learning
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.