提出个性化联邦学习新方法，解决各设备约束不一的问题。
On Performance Guarantees for Federated Learning with Personalized Constraints
- 每台设备维护其他设备变量的交叉估计，本地更新并惩罚自身不可行性。
- 理论证明：收敛速度为子优性 $\mathcal{O}(ε^{-2})$，个体不可行性 $\mathcal{O}(ε^{-1})$。
- 无需共享约束信息，适合资源异构场景，如移动端个性化模型训练。
联邦学习（FL）是一种高效的分布式学习框架，适用于多代理系统。尽管标准FL处理无约束或全局约束问题，但实际应用中常存在异构资源或模型约束，导致每个代理具有独立的可行集。本文研究一种个性化约束联邦优化问题，其中每个代理拥有凸的局部目标函数和私有的约束集。提出PC-FedAvg方法：每个代理通过多块本地决策向量维护对其他代理变量的交叉估计；本地更新所有块，仅在自身块中惩罚不可行性。该交叉估计机制实现个性化，无需共识或共享约束信息。理论分析表明，子优性和个体不可行性的通信复杂度分别为 $\mathcal{O}(ε^{-2})$ 和 $\mathcal{O}(ε^{-1})$。在MNIST和CIFAR-10上的初步实验验证了理论结果。
原文摘要 · Abstract (English)
Federated learning (FL) has emerged as a communication-efficient algorithmic framework for distributed learning across multiple agents. While standard FL formulations capture unconstrained or globally constrained problems, many practical settings involve heterogeneous resource or model constraints, leading to optimization problems with agent-specific feasible sets. Here, we study a personalized constrained federated optimization problem in which each agent is associated with a convex local objective and a private constraint set. We propose PC-FedAvg, a method in which each agent maintains cross-estimates of the other agents' variables through a multi-block local decision vector. Each agent updates all blocks locally, penalizing infeasibility only in its own block. Moreover, the cross-estimate mechanism enables personalization without requiring consensus or sharing constraint information among agents. We establish communication-complexity rates of $\mathcal{O}(ε^{-2})$ for suboptimality and $\mathcal{O}(ε^{-1})$ for agent-wise infeasibility. Preliminary experiments on the MNIST and CIFAR-10 datasets validate our theoretical findings.
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