# pFedSOP : Accelerating Training Of Personalized Federated Learning Using Second-Order Optimization

arXiv: https://arxiv.org/abs/2506.07159 · HTML: https://mlsanity.com/paper/2506.07159/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [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)
- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Towards Personalized Federated Learning](https://mlsanity.com/paper/2103.00710/) (2021)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Personalized Federated Learning: A Meta-Learning Approach](https://mlsanity.com/paper/2002.07948/) (2020)
- [Personalized Federated Learning with First Order Model Optimization](https://mlsanity.com/paper/2012.08565/) (2020)
- [FedBABU: Towards Enhanced Representation for Federated Image Classification](https://mlsanity.com/paper/2106.06042/) (2021)
- [FedALA: Adaptive Local Aggregation for Personalized Federated Learning](https://mlsanity.com/paper/2212.01197/) (2022)
- [Federated Learning for Generalization, Robustness, Fairness: A Survey and Benchmark](https://mlsanity.com/paper/2311.06750/) (2023)
- [Personalized Federated Learning with Feature Alignment and Classifier Collaboration](https://mlsanity.com/paper/2306.11867/) (2023)
- [FedCM: Federated Learning with Client-level Momentum](https://mlsanity.com/paper/2106.10874/) (2021)
- [Fast Convergence of Natural Gradient Descent for Overparameterized Neural Networks](https://mlsanity.com/paper/1905.10961/) (2019)
- [FedExP: Speeding Up Federated Averaging via Extrapolation](https://mlsanity.com/paper/2301.09604/) (2023)
- [Generalizable Heterogeneous Federated Cross-Correlation and Instance Similarity Learning](https://mlsanity.com/paper/2309.16286/) (2023)
- [Implicit Gradient Alignment in Distributed and Federated Learning](https://mlsanity.com/paper/2106.13897/) (2021)
- [Distributed estimation of the inverse Hessian by determinantal averaging](https://mlsanity.com/paper/1905.11546/) (2019)
- [On Second-order Optimization Methods for Federated Learning](https://mlsanity.com/paper/2109.02388/) (2021)
- [FedDWA: Personalized Federated Learning with Dynamic Weight Adjustment](https://mlsanity.com/paper/2305.06124/) (2023)
- [SOFIM: Stochastic Optimization Using Regularized Fisher Information Matrix](https://mlsanity.com/paper/2403.02833/) (2024)

## Built on by (most cited first, 1 of 1)

- [Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations](https://mlsanity.com/paper/2604.12968/) (2026)

## Abstract (arXiv)

Personalized Federated Learning (PFL) enables clients to collaboratively train personalized models tailored to their individual objectives, addressing the challenge of model generalization in traditional Federated Learning (FL) due to high data heterogeneity. However, existing PFL methods often require increased communication rounds to achieve the desired performance, primarily due to slow training caused by the use of first-order optimization, which has linear convergence. Additionally, many of these methods increase local computation because of the additional data fed into the model during the search for personalized local models. One promising solution to this slow training is second-order optimization, known for its quadratic convergence. However, employing it in PFL is challenging due to the Hessian matrix and its inverse. In this paper, we propose pFedSOP, which efficiently utilizes second-order optimization in PFL to accelerate the training of personalized models and enhance performance with fewer communication rounds. Our approach first computes a personalized local gradient update using the Gompertz function-based normalized angle between local and global gradient updates, incorporating client-specific global information. We then use a regularized Fisher Information Matrix (FIM), computed from this personalized gradient update, as an approximation of the Hessian to update the personalized models. This FIM-based second-order optimization speeds up training with fewer communication rounds by tackling the challenges with exact Hessian and avoids additional data being fed into the model during the search for personalized local models. Extensive experiments on heterogeneously partitioned image classification datasets with partial client participation demonstrate that pFedSOP outperforms state-of-the-art FL and PFL algorithms.