# Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning

arXiv: https://arxiv.org/abs/2605.18656 · HTML: https://mlsanity.com/paper/2605.18656/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 11 of 11)

- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [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)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [On the Convergence of Local Descent Methods in Federated Learning](https://mlsanity.com/paper/1910.14425/) (2019)
- [Federated Evaluation and Tuning for On-Device Personalization: System Design & Applications](https://mlsanity.com/paper/2102.08503/) (2021)
- [Learning Differentially Private Recurrent Language Models](https://mlsanity.com/paper/1710.06963/) (2017)
- [Optimal Federated Learning for Nonparametric Regression with Heterogeneous Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.06755/) (2024)
- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Optimal estimation in private distributed functional data analysis](https://mlsanity.com/paper/2412.06582/) (2024)

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

- [Personalized Federated Learning via Variance-Aware Nonparametric Empirical Bayes](https://mlsanity.com/paper/2608.09074/) (2026)

## Abstract (arXiv)

Federated Learning is a leading framework for training ML and AI models collaboratively across numerous user devices or databases. We study the trade-offs among estimation accuracy, privacy constraints, and communication cost for differentially private (DP) federated M estimation. The two standard methods in the literature are FedAvg, which may suffer from high federation bias, and FedSGD, which can incur high communication cost. Aimed at improving accuracy at a reduced communication cost, we propose FedHybrid, which uses FedSGD starting with an improved initialization by the FedAvg estimator. We propose FedNewton, which averages local Newton iterations to reduce bias in FedAvg, achieving an estimation accuracy comparable to FedSGD with much fewer communication rounds when the number of clients grows sufficiently slowly. We establish finite sample upper bounds on the mean-squared error rates of the DP versions of these estimators as functions of the number of clients, local sample sizes, privacy budget, and number of iterations. We further derive a minimax lower bound on the MSE of any iterative private federated procedure that provides a benchmark to assess the optimality gap of these methods. We numerically evaluate our methods for training a logistic regression and a neural network on the computer vision datasets MNIST and CIFAR-10.