  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.
