On the Convergence of Federated Averaging under Partial Participation for Over-parameterized Neural Networks

TL;DR

This paper provides theoretical convergence guarantees for federated averaging in over-parameterized neural networks under partial client participation, supported by experimental validation.

Contribution

It establishes the first convergence analysis of FedAvg with partial participation for over-parameterized neural networks, including deep linear and two-layer ReLU models.

Findings

FedAvg converges linearly under partial participation in over-parameterized settings.

Convergence rate depends on the minimum number of participating clients per iteration.

Experimental results validate the theoretical convergence guarantees.

Abstract

Federated learning (FL) is a widely employed distributed paradigm for collaboratively training machine learning models from multiple clients without sharing local data. In practice, FL encounters challenges in dealing with partial client participation due to the limited bandwidth, intermittent connection and strict synchronized delay. Simultaneously, there exist few theoretical convergence guarantees in this practical setting, especially when associated with the non-convex optimization of neural networks. To bridge this gap, we focus on the training problem of federated averaging (FedAvg) method for two canonical models: a deep linear network and a two-layer ReLU network. Under the over-parameterized assumption, we provably show that FedAvg converges to a global minimum at a linear rate $\mathcal{O}\left((1-\frac{min_{i \in [t]}|S_i|}{N^2})^t\right)$ after $t$ iterations, where $N$ is the number of clients and $|S_i|$ is the number of the participated clients in the $i$-th iteration. Experimental evaluations confirm our theoretical results.