TY - JOUR
T1 - Review of Mathematical Optimization in Federated Learning
AU - Yang , Shusen
AU - Zhao , Fangyuan
AU - Zhou , Zihao
AU - Shi , Liang
AU - Ren , Xuebin
AU - Xu , Zongben
JO - CSIAM Transactions on Applied Mathematics
VL - 2
SP - 207
EP - 249
PY - 2025
DA - 2025/05
SN - 6
DO - http://doi.org/10.4208/csiam-am.SO-2024-0023
UR - https://global-sci.org/intro/article_detail/csiam-am/24085.html
KW - Federated learning, distributed optimization, convergence analysis, error bounds.
AB - <p style="text-align: justify;">Federated learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL
aims to collaboratively optimize aggregate objective functions over distributed datasets while satisfying a variety of privacy and system constraints. Different from conventional distributed optimization methods, FL needs to address several specific issues
(e.g. non-i.i.d. data and differential private noises), which pose a set of new challenges
in the problem formulation, algorithm design, and convergence analysis. In this paper, we will systematically review existing FL optimization research including their
assumptions, formulations, methods, and theoretical results. Potential future directions are also discussed.</p>