Federated Learning as Variational Inference: A Scalable Expectation Propagation Approach

Han Guo, Philip Greengard, Hongyi Wang, Andrew Gelman, Yoon Kim, Eric Xing

Keywords: federated learning, variational inference, expectation propagation

Abstract: The canonical formulation of federated learning treats it as a distributed optimization problem where the model parameters are optimized against a global loss function that decomposes across client loss functions. A recent alternative formulation instead treats federated learning as a distributed inference problem, where the goal is to infer a global posterior from partitioned client data (Al-Shedivat et al., 2021). This paper extends the inference view and describes a variational inference formulation of federated learning where the goal is to find a global variational posterior that well-approximates the true posterior. This naturally motivates an expectation propagation approach to federated learning (FedEP), where approximations to the global posterior are iteratively refined through probabilistic message-passing between the central server and the clients. We conduct an extensive empirical study across various algorithmic considerations and describe practical strategies for scaling up expectation propagation to the modern federated setting. We apply FedEP on standard federated learning benchmarks and find that it outperforms strong baselines in terms of both convergence speed and accuracy.

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TL;DR: This work introduces a probabilistic message-passing algorithm for federated learning based on expectation propagation (FedEP) and studies algorithmic considerations to scale up classic expectation propagation to modern federated learning settings.