# Locally Differentially Private Online Federated Learning With Correlated Noise

arXiv: https://arxiv.org/abs/2411.18752 · HTML: https://mlsanity.com/paper/2411.18752/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 27 Nov 2024.

## Builds on (most cited first, 25 of 25)

- [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)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Practical and Private (Deep) Learning without Sampling or Shuffling](https://mlsanity.com/paper/2103.00039/) (2021)
- [Improved Differential Privacy for SGD via Optimal Private Linear Operators on Adaptive Streams](https://mlsanity.com/paper/2202.08312/) (2022)
- [Wireless Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2002.05151/) (2020)
- [(Amplified) Banded Matrix Factorization: A unified approach to private training](https://mlsanity.com/paper/2306.08153/) (2023)
- [Improved Dynamic Regret for Non-degenerate Functions](https://mlsanity.com/paper/1608.03933/) (2016)
- [Calculus of the exponent of Kurdyka-Lojasiewicz inequality and its applications to linear convergence of first-order methods](https://mlsanity.com/paper/1602.02915/) (2016)
- [The Price of Differential Privacy under Continual Observation](https://mlsanity.com/paper/2112.00828/) (2021)
- [Online Non-Convex Learning: Following the Perturbed Leader is Optimal](https://mlsanity.com/paper/1903.08110/) (2019)
- [Almost Tight Error Bounds on Differentially Private Continual Counting](https://mlsanity.com/paper/2211.05006/) (2022)
- [Gradient methods for convex minimization: better rates under weaker conditions](https://mlsanity.com/paper/1303.4645/) (2013)
- [A Unified Approach to Error Bounds for Structured Convex Optimization Problems](https://mlsanity.com/paper/1512.03518/) (2015)
- [Gradient Descent with Linearly Correlated Noise: Theory and Applications to Differential Privacy](https://mlsanity.com/paper/2302.01463/) (2023)
- [Differentially Private Distributed Online Learning](https://mlsanity.com/paper/1505.06556/) (2015)
- [On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning](https://mlsanity.com/paper/2308.14606/) (2023)
- [Improving Dynamic Regret in Distributed Online Mirror Descent Using Primal and Dual Information](https://mlsanity.com/paper/2112.03504/) (2021)
- [A Communication-Efficient Adaptive Algorithm for Federated Learning under Cumulative Regret](https://mlsanity.com/paper/2301.08869/) (2023)
- [Linear Speedup of Incremental Aggregated Gradient Methods on Streaming Data](https://mlsanity.com/paper/2309.04980/) (2023)
- [Distributed Online Private Learning of Convex Nondecomposable Objectives](https://mlsanity.com/paper/2206.07944/) (2022)
- [Distributed Online Non-convex Optimization with Composite Regret](https://mlsanity.com/paper/2209.10105/) (2022)
- [Differential Private Discrete Noise Adding Mechanism: Conditions, Properties and Optimization](https://mlsanity.com/paper/2203.10323/) (2022)

## Built on by (most cited first, 6 of 6)

- [Back to Square Roots: An Optimal Bound on the Matrix Factorization Error for Multi-Epoch Differentially Private SGD](https://mlsanity.com/paper/2505.12128/) (2025)
- [FedCanon: Non-Convex Composite Federated Learning with Efficient Proximal Operation on Heterogeneous Data](https://mlsanity.com/paper/2504.11903/) (2025)
- [Learning Rate Scheduling with Matrix Factorization for Private Training](https://mlsanity.com/paper/2511.17994/) (2025)
- [Generalization Error Analysis for Attack-Free and Byzantine-Resilient Decentralized Learning with Data Heterogeneity](https://mlsanity.com/paper/2506.09438/) (2025)
- [Cocoon: A System Architecture for Differentially Private Training with Correlated Noises](https://mlsanity.com/paper/2510.07304/) (2025)
- [Tackling Privacy Heterogeneity in Differentially Private Federated Learning](https://mlsanity.com/paper/2602.22633/) (2026)

## Abstract (arXiv)

We introduce a locally differentially private (LDP) algorithm for online federated learning that employs temporally correlated noise to improve utility while preserving privacy. To address challenges posed by the correlated noise and local updates with streaming non-IID data, we develop a perturbed iterate analysis that controls the impact of the noise on the utility. Moreover, we demonstrate how the drift errors from local updates can be effectively managed for several classes of nonconvex loss functions. Subject to an (ε,δ)-LDP budget, we establish a dynamic regret bound that quantifies the impact of key parameters and the intensity of changes in the dynamic environment on the learning performance. Numerical experiments confirm the efficacy of the proposed algorithm.