Abstract: 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 both the server and 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 empirical results where the benefit of the client adaptivity is shown in various FL scenarios. In particular, our proposed method achieves TOP-1 accuracy in 73\% and TOP-2 accuracy in 100\% of the experiments considered without additional tuning.