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Standard federated learning (FL) algorithms typically require multiple rounds of communication between the server and the clients, which has several drawbacks, including requiring constant network connectivity, repeated investment of computational resources, and susceptibility to privacy attacks. One-Shot FL is a new paradigm that aims to address this challenge by enabling the server to train a global model in a single round of communication. In this work, we present FedFisher, a novel algorithm for one-shot FL that makes use of Fisher information matrices computed on local client models, motivated by a Bayesian perspective of FL. First, we theoretically analyze FedFisher for two-layer over-parameterized ReLU neural networks and show that the error of our one-shot FedFisher global model becomes vanishingly small as the width of the neural networks and amount of local training at clients increases. Next, we propose practical variants of FedFisher using the diagonal Fisher and K-FAC approximation for the full Fisher and highlight their communication and compute efficiency for FL. Finally, we conduct extensive experiments on various datasets, which show that these variants of FedFisher consistently improve over competing baselines. 

Decentralized learning has emerged as an alternative method to the popular parameter-server framework which suffers from high communication burden, single-point failure and scalability issues due to the need of a central server. However, most existing works focus on a single shared model for all workers regardless of the data heterogeneity problem, rendering the resulting model performing poorly on individual workers. In this work, we propose a novel personalized decentralized learning algorithm named DePRL via shared representations. Our algorithm relies on ideas from representation learning theory to learn a low-dimensional global representation collaboratively among all workers in a fully decentralized manner, as well as a user-specific low-dimensional local head leading to a personalized solution for each worker. We show that DePRL achieves, for the first time, a provable \textit{linear speedup for convergence} with general non-linear representations (i.e., the convergence rate is improved linearly with respect to the number of workers). Experimental results support our theoretical findings showing the superiority of our method in data heterogeneous environments.

 

Dealing with data heterogeneity is a key challenge in the theoretical analysis of federated learning (FL) algorithms. In the literature, gradient divergence is often used as the sole metric for data heterogeneity. However, we observe that the gradient divergence cannot fully characterize the impact of the data heterogeneity in Federated Averaging (FedAvg) even for the quadratic objective functions. This limitation leads to an overestimate of the communication complexity. Motivated by this observation, we propose a new analysis framework based on the difference between the minima of the global objective function and the minima of the local objective functions. Using the new framework, we derive a tighter convergence upper bound for heterogeneous quadratic objective functions. The theoretical results reveal new insights into the impact of the data heterogeneity on the convergence of FedAvg and provide a deeper understanding of the two-stage learning rates. Experimental results using non-IID data partitions validate the theoretical findings. 

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.