We consider a federated learning (FL) system consisting of multiple clients and a server, where the clients aim to collaboratively learn a common decision model from their distributed data. Unlike the conventional FL framework that assumes the client's data is static, we consider scenarios where the clients' data distributions may be reshaped by the deployed decision model. In this work, we leverage the idea of distribution shift mappings in performative prediction to formalize this model-dependent data distribution shift and propose a performative federated learning framework. We first introduce necessary and sufficient conditions for the existence of a unique performative stable solution and characterize its distance to the performative optimal solution. Then we propose the performative FedAvg algorithm and show that it converges to the performative stable solution at a rate of O(1/T) under both full and partial participation schemes. In particular, we use novel proof techniques and show how the clients' heterogeneity influences the convergence. Numerical results validate our analysis and provide valuable insights into real-world applications.

翻译：我们考虑一个由多个客户端和服务器组成的联邦学习系统，其中客户端旨在从其分布式数据中协作学习一个共同的决策模型。与假设客户端数据静态的传统联邦学习框架不同，我们考虑客户端数据分布可能受所部署决策模型影响的场景。本文利用性能化预测中的分布偏移映射思想来形式化这种模型依赖的数据分布偏移，并提出一个性能化联邦学习框架。我们首先给出存在唯一性能化稳定解的必要与充分条件，并刻画其与性能化最优解之间的距离。随后，我们提出性能化FedAvg算法，并证明在完全参与和部分参与两种方案下，该算法均以O(1/T)的速率收敛至性能化稳定解。特别地，我们采用新颖的证明技术，揭示了客户端异构性对收敛性的影响。数值结果验证了我们的分析，并为实际应用提供了有价值的见解。