# Personalized Federated Learning of Probabilistic Models: A PAC-Bayesian Approach

arXiv: https://arxiv.org/abs/2401.08351 · HTML: https://mlsanity.com/paper/2401.08351/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 58 references that are in the map.
- First posted on arXiv 16 Jan 2024.

## Builds on (most cited first, 30 of 39)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [Federated Learning with Matched Averaging](https://mlsanity.com/paper/2002.06440/) (2020)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Differential Privacy Has Disparate Impact on Model Accuracy](https://mlsanity.com/paper/1905.12101/) (2019)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Federated Optimization:Distributed Optimization Beyond the Datacenter](https://mlsanity.com/paper/1511.03575/) (2015)
- [Federated Multi-Task Learning under a Mixture of Distributions](https://mlsanity.com/paper/2108.10252/) (2021)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [Survey of Personalization Techniques for Federated Learning](https://mlsanity.com/paper/2003.08673/) (2020)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [Generalization in Adaptive Data Analysis and Holdout Reuse](https://mlsanity.com/paper/1506.02629/) (2015)
- [Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors](https://mlsanity.com/paper/1712.09376/) (2017)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [Federated Learning via Posterior Averaging: A New Perspective and Practical Algorithms](https://mlsanity.com/paper/2010.05273/) (2020)
- [Meta-Learning by Adjusting Priors Based on Extended PAC-Bayes Theory](https://mlsanity.com/paper/1711.01244/) (2017)
- [Personalized Federated Learning with Gaussian Processes](https://mlsanity.com/paper/2106.15482/) (2021)
- [A PAC-Bayesian bound for Lifelong Learning](https://mlsanity.com/paper/1311.2838/) (2013)

## Built on by (most cited first, 5 of 5)

- [Overcoming label shift with target-aware federated learning](https://mlsanity.com/paper/2411.03799/) (2024)
- [Decentralized Federated Learning of Probabilistic Generative Classifiers](https://mlsanity.com/paper/2507.17285/) (2025)
- [Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning](https://mlsanity.com/paper/2509.10132/) (2025)
- [Scaling Law Analysis in Federated Learning: How to Select the Optimal Model Size?](https://mlsanity.com/paper/2511.12188/) (2025)
- [Closing the Generalization Gap in Parameter-efficient Federated Edge Learning](https://mlsanity.com/paper/2511.23282/) (2025)

## Abstract (arXiv)

Federated Learning (FL) aims to infer a shared model from private and decentralized data stored by multiple clients. Personalized FL (PFL) enhances the model's fit for each client by adapting the global model to the clients. A significant level of personalization is required for highly heterogeneous clients but can be challenging to achieve, especially when clients' datasets are small. To address this issue, we introduce the PAC-PFL framework for PFL of probabilistic models. PAC-PFL infers a shared hyper-posterior and treats each client's posterior inference as the personalization step. Unlike previous PFL algorithms, PAC-PFL does not regularize all personalized models towards a single shared model, thereby greatly enhancing its personalization flexibility. By establishing and minimizing a PAC-Bayesian generalization bound on the average true loss of clients, PAC-PFL effectively mitigates overfitting even in data-poor scenarios. Additionally, PAC-PFL provides generalization bounds for new clients joining later. PAC-PFL achieves accurate and well-calibrated predictions, as supported by our experiments.