系统梳理联邦学习优化的数学方法与挑战
Review of Mathematical Optimization in Federated Learning
- 从数学角度综述联邦学习的优化框架与约束
- 涵盖非独立同分布数据与差分隐私等核心挑战
- 适合关注算法理论与未来方向的研究者
联邦学习（FL）已成为应用数学与信息科学领域的热门跨学科研究方向。数学上，FL旨在在分布式数据集上协同优化全局目标函数，同时满足各类隐私与系统约束。与传统分布式优化方法不同，FL需应对非独立同分布数据分布和差分隐私噪声等特定问题，这为问题建模、算法设计与收敛性分析带来了新挑战。本文系统回顾现有联邦学习优化研究，包括其假设、公式、方法与理论成果，并探讨潜在的未来方向。
原文摘要 · Abstract (English)
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 distributions 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.
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