Title: Communication-Efficient and Drift-Robust Federated Learning via Elastic Net. Abstract: Federated learning (FL) is a distributed method to train a global model over a set of local clients while keeping data localized, which reduces risks of privacy and security. FL framework faces important challenges including expensive communication cost and client drift problem. Leveraging the elastic net, we propose a communication-efficient and drift-robust FL framework to improve the communication efficiency and resolve the client drift problem. We repurpose two types of the elastic net regularizers (i.e., $\ell_1$ and $\ell_2$ penalties on the local model updates): (1) the $\ell_1$-norm regularizer sparsifies the local updates to enhance the communication efficiency and (2) the $\ell_2$-norm regularizer attempts to resolve the client drift problem by limiting the impact of drifting local updates due to data heterogeneity. Our framework is general; hence, it can be integrated with prior FL techniques, e.g., FedAvg, FedProx, SCAFFOLD, and FedDyn. We show that our framework effectively resolves the communication cost problem and the client drift problem simultaneously.