Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms (2010.05273v4)

Abstract: Federated learning is typically approached as an optimization problem, where the goal is to minimize a global loss function by distributing computation across client devices that possess local data and specify different parts of the global objective. We present an alternative perspective and formulate federated learning as a posterior inference problem, where the goal is to infer a global posterior distribution by having client devices each infer the posterior of their local data. While exact inference is often intractable, this perspective provides a principled way to search for global optima in federated settings. Further, starting with the analysis of federated quadratic objectives, we develop a computation- and communication-efficient approximate posterior inference algorithm -- federated posterior averaging (FedPA). Our algorithm uses MCMC for approximate inference of local posteriors on the clients and efficiently communicates their statistics to the server, where the latter uses them to refine a global estimate of the posterior mode. Finally, we show that FedPA generalizes federated averaging (FedAvg), can similarly benefit from adaptive optimizers, and yields state-of-the-art results on four realistic and challenging benchmarks, converging faster, to better optima.

• The paper introduces a novel perspective by treating federated learning as a posterior inference problem to overcome data heterogeneity and communication constraints.
• It employs Markov Chain Monte Carlo methods for local posterior inference, aggregating statistical insights to form a robust global posterior estimate.
• Empirical evaluations across benchmarks show FedPA achieves faster convergence and improved accuracy compared to traditional methods like FedAvg and MIME.

Federated Learning via Posterior Averaging: An Expert Overview

The paper "Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms" proposes a novel approach to federated learning (FL) by reconceptualizing it as a posterior inference problem rather than a conventional optimization challenge. This shift in perspective aims to address persistent issues in federated learning, particularly those arising from data heterogeneity and communication constraints among distributed clients.

Novel Perspective on Federated Learning

Federated learning traditionally focuses on optimizing a global loss function through distributed computations across client devices. This method inherently involves synchronizing weights and updates between clients and a central server while addressing challenges like non-i.i.d data distribution and the high cost of communication. Canonical methods like Federated Averaging (\FedAvg) have enjoyed widespread application due to their simplicity and effectiveness. However, these techniques often suffer from convergence issues due to biased updates resulting from the heterogeneity of client data.

The authors of this paper introduce a compelling alternative: treating federated learning as a posterior inference problem. This allows the distribution of computation to infer global posterior distributions by aggregating local posterior statistics computed at the client level.

Federated Posterior Averaging (\FedPA)

To operationalize this idea, the authors present Federated Posterior Averaging (\FedPA), which employs Markov Chain Monte Carlo (MCMC) methods to perform local posterior inference at client sites. \FedPA efficiently communicates these local statistics to the central server, where they are aggregated to refine a global posterior mode estimate. Notably, \FedPA represents a generalization of \FedAvg, inheriting its structural efficiency while aiming for more accurate convergence by correcting client update biases through posterior modes.

The authors demonstrate that \FedPA can converge faster and achieve more optimal solutions than traditional methods by better integrating local computation and statistical inference.

Empirical Evaluation and Results

The paper reports empirical evaluations across four complex benchmark tasks: EMNIST handwriting recognition, CIFAR-100 image classification, and two tasks involving the StackOverflow dataset—next-word prediction and tag prediction. In these settings, \FedPA achieved state-of-the-art results, showing improvements in terms of convergence speed and final model accuracy over strong baseline approaches including \FedAvg and \MIME.

Notably, while \FedPA provided marginal improvements in some tasks, such as a 0.5% accuracy increase over existing solutions for EMNIST, it substantially improved learning speed and robustness against client data heterogeneity.

Practical and Theoretical Implications

Practically, this work suggests an alternative route to federated learning that broadens the design space beyond purely optimization-centric techniques. The potential for statistical modes to better capture data heterogeneity presents an avenue for improved algorithms in distributed learning environments.

Theoretically, the connection between distributed posterior inference and federated optimization provides fertile ground for further research. The implications for privacy, particularly leveraging the statistical security inherent in posterior sampling, invite intriguing explorations in privacy-preserving machine learning.

Future Directions

Future research could explore varying sampling strategies, sophisticated covariance estimation techniques, and expand the Bayesian framework to encompass more complex deep learning scenarios. An additional avenue could investigate adaptive switching mechanisms from burn-in to sampling phases, potentially optimizing \FedPA’s efficacy in real-world applications.

Overall, this paper contributes significantly to federated learning literature by reimagining one of its core problems, offering promising alternatives to existing paradigms while pushing the boundaries of what efficient distributed learning can achieve.