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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (3): 509-528.doi: 10.3969/j.issn.1005-3085.2025.03.008doi: 32411.14.1005-3085.2025.03.008

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部分用户参与场景下的基于牛顿法的联邦学习算法

曹子龙,    郭  骁,   张  海   

  1. 西北大学数学学院，西安 710127
  • 收稿日期:2022-10-15 接受日期:2023-03-29 出版日期:2025-06-15 发布日期:2025-06-15
  • 基金资助:
    国家自然科学基金–广东省大数据重大项目 (U1811461).

Federated Learning Algorithm Based on Newton's Method under the Partial Participation Scheme

CAO Zilong,   GUO Xiao,   ZHANG Hai   

  1. School of Mathematics, Northwest University, Xi'an 710127
  • Received:2022-10-15 Accepted:2023-03-29 Online:2025-06-15 Published:2025-06-15
  • Supported by:
    The National Natural Science Foundation of China--Big Data Major Project of Guangdong Province (U1811461).

摘要：

联邦学习是应对数据孤岛和隐私保护问题的新型分布式学习框架。关注二阶梯度联邦学习算法，针对更为实际的仅能有部分用户参与联邦学习任务的假设情形，开展对于联邦学习牛顿算法的研究。从理论上证明了算法的收敛。通过利用McDiarmid不等式，理论上解释了参与用户的数量与算法的收敛速度以及最终的收敛误差之间的权衡关系。实验结果表明算法能够快速高效地收敛，有效降低联邦学习的通信成本，证明了算法的有效、实用性和理论的正确性。

关键词: 联邦学习, 牛顿法, 收敛性, 分布式计算, 通信有效

Abstract:

Federated learning is a new distributed learning framework to deal with data isolation and privacy protection. This paper focuses on the second-order gradient federated learning algorithm. It carries out the research on the federated learning Newton's algorithm for the more practical scheme that only some users can participate in the federated learning task. The convergence of the algorithm is proved theoretically. By using the McDiarmid inequality, the trade-off of the number of participating users, the convergence speed of the algorithm and the final convergence error are theoretically explained. The experimental results show that the algorithm can converge quickly and efficiently, effectively reduce the communication cost of federated learning, and prove the effectiveness, practicality and theoretical correctness of the algorithm.

Key words: federated learning, Newton's method, convergence, distributed computing, communication effectiveness

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