  In Federated Learning (FL) client devices connected over the internet
collaboratively train a machine learning model without sharing their private
data with a central server or with other clients. The seminal Federated
Averaging (FedAvg) algorithm trains a single global model by performing rounds
of local training on clients followed by model averaging. FedAvg can improve
the communication-efficiency of training by performing more steps of Stochastic
Gradient Descent (SGD) on clients in each round. However, client data in
real-world FL is highly heterogeneous, which has been extensively shown to slow
model convergence and harm final performance when $K > 1$ steps of SGD are
performed on clients per round. In this work we propose decaying $K$ as
training progresses, which can jointly improve the final performance of the FL
model whilst reducing the wall-clock time and the total computational cost of
training compared to using a fixed $K$. We analyse the convergence of FedAvg
with decaying $K$ for strongly-convex objectives, providing novel insights into
the convergence properties, and derive three theoretically-motivated decay
schedules for $K$. We then perform thorough experiments on four benchmark FL
datasets (FEMNIST, CIFAR100, Sentiment140, Shakespeare) to show the real-world
benefit of our approaches in terms of real-world convergence time,
computational cost, and generalisation performance.
