# Decentralized Personalized Federated Learning: Lower Bounds and Optimal Algorithm for All Personalization Modes

arXiv: https://arxiv.org/abs/2107.07190 · HTML: https://mlsanity.com/paper/2107.07190/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2021.

## Built on by (most cited first, 13 of 13)

- [Personalized Decentralized Federated Learning with Knowledge Distillation](https://mlsanity.com/paper/2302.12156/) (2023)
- [Decentralized Directed Collaboration for Personalized Federated Learning](https://mlsanity.com/paper/2405.17876/) (2024)
- [Towards More Suitable Personalization in Federated Learning via Decentralized Partial Model Training](https://mlsanity.com/paper/2305.15157/) (2023)
- [PersA-FL: Personalized Asynchronous Federated Learning](https://mlsanity.com/paper/2210.01176/) (2022)
- [FedSPD: A Soft-clustering Approach for Personalized Decentralized Federated Learning](https://mlsanity.com/paper/2410.18862/) (2024)
- [Revisiting LocalSGD and SCAFFOLD: Improved Rates and Missing Analysis](https://mlsanity.com/paper/2501.04443/) (2025)
- [Smart Sampling: Helping from Friendly Neighbors for Decentralized Federated Learning](https://mlsanity.com/paper/2407.04460/) (2024)
- [FedPeWS: Personalized Warmup via Subnetworks for Enhanced Heterogeneous Federated Learning](https://mlsanity.com/paper/2410.03042/) (2024)
- [Federated Learning Can Find Friends That Are Advantageous](https://mlsanity.com/paper/2402.05050/) (2024)
- [Collaborative and Efficient Personalization with Mixtures of Adaptors](https://mlsanity.com/paper/2410.03497/) (2024)
- [S-VOTE: Similarity-based Voting for Client Selection in Decentralized Federated Learning](https://mlsanity.com/paper/2501.19279/) (2025)
- [Personalized and Resilient Distributed Learning Through Opinion Dynamics](https://mlsanity.com/paper/2505.14081/) (2025)
- [Robust Decentralized Personalized Federated Learning via Prediction-Constrained Neighborhood Collaboration](https://mlsanity.com/paper/2609.07312/) (2026)

## Abstract (arXiv)

This paper considers the problem of decentralized, personalized federated learning. For centralized personalized federated learning, a penalty that measures the deviation from the local model and its average, is often added to the objective function. However, in a decentralized setting this penalty is expensive in terms of communication costs, so here, a different penalty - one that is built to respect the structure of the underlying computational network - is used instead. We present lower bounds on the communication and local computation costs for this problem formulation and we also present provably optimal methods for decentralized personalized federated learning. Numerical experiments are presented to demonstrate the practical performance of our methods.