  Federated learning (FL) is a distributed machine learning framework where the
global model of a central server is trained via multiple collaborative steps by
participating clients without sharing their data. While being a flexible
framework, where the distribution of local data, participation rate, and
computing power of each client can greatly vary, such flexibility gives rise to
many new challenges, especially in the hyperparameter tuning on the client
side. We propose $\Delta$-SGD, a simple step size rule for SGD that enables
each client to use its own step size by adapting to the local smoothness of the
function each client is optimizing. We provide theoretical and empirical
results where the benefit of the client adaptivity is shown in various FL
scenarios.
