# Sharp Gaussian approximations for Decentralized Federated Learning

arXiv: https://arxiv.org/abs/2505.08125 · HTML: https://mlsanity.com/paper/2505.08125/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 93 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 30 of 43)

- [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)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Tackling the Objective Inconsistency Problem in Heterogeneous Federated Optimization](https://mlsanity.com/paper/2007.07481/) (2020)
- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)
- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Attack of the Tails: Yes, You Really Can Backdoor Federated Learning](https://mlsanity.com/paper/2007.05084/) (2020)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Asynchronous Federated Optimization](https://mlsanity.com/paper/1903.03934/) (2019)
- [Tighter Theory for Local SGD on Identical and Heterogeneous Data](https://mlsanity.com/paper/1909.04746/) (2019)
- [Don't Use Large Mini-Batches, Use Local SGD](https://mlsanity.com/paper/1808.07217/) (2018)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Minibatch vs Local SGD for Heterogeneous Distributed Learning](https://mlsanity.com/paper/2006.04735/) (2020)
- [On a Formal Model of Safe and Scalable Self-driving Cars](https://mlsanity.com/paper/1708.06374/) (2017)
- [Local SGD with Periodic Averaging: Tighter Analysis and Adaptive Synchronization](https://mlsanity.com/paper/1910.13598/) (2019)
- [Blockchained On-Device Federated Learning](https://mlsanity.com/paper/1808.03949/) (2018)
- [Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chains](https://mlsanity.com/paper/1707.06386/) (2017)
- [Decentralized Federated Learning: A Survey and Perspective](https://mlsanity.com/paper/2306.01603/) (2023)
- [Peer-to-peer Federated Learning on Graphs](https://mlsanity.com/paper/1901.11173/) (2019)
- [Communication-efficient distributed SGD with Sketching](https://mlsanity.com/paper/1903.04488/) (2019)
- [Statistical Inference for Model Parameters in Stochastic Gradient Descent](https://mlsanity.com/paper/1610.08637/) (2016)
- [Sharp Bounds for Federated Averaging (Local SGD) and Continuous Perspective](https://mlsanity.com/paper/2111.03741/) (2021)
- [Online Covariance Matrix Estimation in Stochastic Gradient Descent](https://mlsanity.com/paper/2002.03979/) (2020)
- [Adaptive and Robust Multi-Task Learning](https://mlsanity.com/paper/2202.05250/) (2022)
- [Central Server Free Federated Learning over Single-sided Trust Social Networks](https://mlsanity.com/paper/1910.04956/) (2019)
- [Optimal and instance-dependent guarantees for Markovian linear stochastic approximation](https://mlsanity.com/paper/2112.12770/) (2021)
- [Normal Approximation for Stochastic Gradient Descent via Non-Asymptotic Rates of Martingale CLT](https://mlsanity.com/paper/1904.02130/) (2019)

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

- [Sharp asymptotic theory for Q-learning with LDTZ learning rate and its generalization](https://mlsanity.com/paper/2604.04218/) (2026)

## Abstract (arXiv)

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation results for local SGD and explore their implications. First, we prove a Berry-Esseen theorem for the final local SGD iterates, enabling valid multiplier bootstrap procedures. Second, motivated by robustness considerations, we introduce two distinct time-uniform Gaussian approximations for the entire trajectory of local SGD. The time-uniform approximations support Gaussian bootstrap-based tests for detecting adversarial attacks. Extensive simulations are provided to support our theoretical results.