# Personalized Federated Learning with Exact Stochastic Gradient Descent

arXiv: https://arxiv.org/abs/2202.09848 · HTML: https://mlsanity.com/paper/2202.09848/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 57 references that are in the map.
- First posted on arXiv 20 Feb 2022.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [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)
- [Adaptive Federated Optimization](https://mlsanity.com/paper/2003.00295/) (2020)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming](https://mlsanity.com/paper/1309.5549/) (2013)
- [Ditto: Fair and Robust Federated Learning Through Personalization](https://mlsanity.com/paper/2012.04221/) (2020)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning with Personalization Layers](https://mlsanity.com/paper/1912.00818/) (2019)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [Federated Learning on Non-IID Data: A Survey](https://mlsanity.com/paper/2106.06843/) (2021)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [Parallel Restarted SGD with Faster Convergence and Less Communication: Demystifying Why Model Averaging Works for Deep Learning](https://mlsanity.com/paper/1807.06629/) (2018)
- [Improving Federated Learning Personalization via Model Agnostic Meta Learning](https://mlsanity.com/paper/1909.12488/) (2019)
- [Personalized Federated Learning using Hypernetworks](https://mlsanity.com/paper/2103.04628/) (2021)
- [FedHealth: A Federated Transfer Learning Framework for Wearable Healthcare](https://mlsanity.com/paper/1907.09173/) (2019)
- [FedBABU: Towards Enhanced Representation for Federated Image Classification](https://mlsanity.com/paper/2106.06042/) (2021)
- [On the Linear Speedup Analysis of Communication Efficient Momentum SGD for Distributed Non-Convex Optimization](https://mlsanity.com/paper/1905.03817/) (2019)
- [cpSGD: Communication-efficient and differentially-private distributed SGD](https://mlsanity.com/paper/1805.10559/) (2018)
- [Federated Meta-Learning with Fast Convergence and Efficient Communication](https://mlsanity.com/paper/1802.07876/) (2018)
- [Federated Evaluation of On-device Personalization](https://mlsanity.com/paper/1910.10252/) (2019)
- [Salvaging Federated Learning by Local Adaptation](https://mlsanity.com/paper/2002.04758/) (2020)
- [Scheduling Policies for Federated Learning in Wireless Networks](https://mlsanity.com/paper/1908.06287/) (2019)

## Built on by (most cited first, 4 of 4)

- [Confidence-aware Personalized Federated Learning via Variational Expectation Maximization](https://mlsanity.com/paper/2305.12557/) (2023)
- [Distributed Learning over Networks with Graph-Attention-Based Personalization](https://mlsanity.com/paper/2305.13041/) (2023)
- [Personalized Federated Learning on Heterogeneous and Long-Tailed Data via Expert Collaborative Learning](https://mlsanity.com/paper/2408.02019/) (2024)
- [Guided Model Merging for Hybrid Data Learning: Leveraging Centralized Data to Refine Decentralized Models](https://mlsanity.com/paper/2503.20138/) (2025)

## Abstract (arXiv)

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained includes a set of common weights for all clients, and a set of personalized weights that are specific to each client. At each optimization round, randomly selected clients perform multiple full gradient-descent updates over their client-specific weights towards optimizing the loss function on their own datasets, without updating the common weights. This procedure is energy-efficient since it has low computational cost per client. At the final update of each round, each client computes the joint gradient over both the client-specific and the common weights and returns the gradient of common weights to the server, which allows to perform an exact SGD step over the full set of weights in a distributed manner. For the overall optimization scheme, we rigorously prove convergence, even in non-convex settings such as those encountered when training neural networks, with a rate of O left (frac1√T right ) with respect to communication rounds T. In practice, PFLEGO exhibits substantially lower per-round wall-clock time, used as a proxy for energy. Our theoretical guarantees translate to superior performance in practice against baselines such as FedAvg and FedPer, as evaluated in several multi-class classification datasets, in particular, Omniglot, CIFAR-10, MNIST, Fashion-MNIST, and EMNIST.