Title: FedExP: Speeding Up Federated Averaging via Extrapolation. Abstract: Federated Averaging (FedAvg) remains the most popular algorithm for Federated Learning (FL) optimization due to its simple implementation, stateless nature, and privacy guarantees combined with secure aggregation. Recent work has sought to generalize the vanilla averaging in FedAvg to a generalized gradient descent step by treating client updates as pseudo-gradients and using a server step size. While the use of a server step size has been shown to provide performance improvement theoretically, the practical benefit of the server step size has not been seen in most existing works. In this work, we present FedExP, a method to adaptively determine the server step size in FL based on dynamically varying pseudo-gradients throughout the FL process. We begin by considering the overparameterized convex regime, where we reveal an interesting similarity between FedAvg and the Projection Onto Convex Sets (POCS) algorithm. We then show how FedExP can be motivated as a novel extension to the extrapolation mechanism that is used to speed up POCS. Our theoretical analysis later also discusses the implications of FedExP in underparameterized and non-convex settings. Experimental results show that FedExP consistently converges faster than FedAvg and competing baselines on a range of realistic FL datasets. 