# Private Decentralized Optimization with Noise Reduction and Bias Correction

arXiv: https://arxiv.org/abs/2609.27658 · HTML: https://mlsanity.com/paper/2609.27658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Momentum-Based Variance Reduction in Non-Convex SGD](https://mlsanity.com/paper/1905.10018/) (2019)
- [R'enyi Differential Privacy of the Sampled Gaussian Mechanism](https://mlsanity.com/paper/1908.10530/) (2019)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [Revisiting Gradient Clipping: Stochastic bias and tight convergence guarantees](https://mlsanity.com/paper/2305.01588/) (2023)
- [Exact Diffusion for Distributed Optimization and Learning --- Part I: Algorithm Development](https://mlsanity.com/paper/1702.05122/) (2017)
- [A Unified and Refined Convergence Analysis for Non-Convex Decentralized Learning](https://mlsanity.com/paper/2110.09993/) (2021)
- [On the Influence of Bias-Correction on Distributed Stochastic Optimization](https://mlsanity.com/paper/1903.10956/) (2019)
- [Privacy Amplification by Decentralization](https://mlsanity.com/paper/2012.05326/) (2020)
- [Efficient Privacy-Preserving Stochastic Nonconvex Optimization](https://mlsanity.com/paper/1910.13659/) (2019)
- [Muffliato: Peer-to-Peer Privacy Amplification for Decentralized Optimization and Averaging](https://mlsanity.com/paper/2206.05091/) (2022)
- [A Hybrid Variance-Reduced Method for Decentralized Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2102.06752/) (2021)
- [Momentum Tracking: Momentum Acceleration for Decentralized Deep Learning on Heterogeneous Data](https://mlsanity.com/paper/2209.15505/) (2022)
- [Differentially Private Adaptive Optimization with Delayed Preconditioners](https://mlsanity.com/paper/2212.00309/) (2022)
- [The Privacy Power of Correlated Noise in Decentralized Learning](https://mlsanity.com/paper/2405.01031/) (2024)
- [Proximal Stochastic Recursive Momentum Methods for Nonconvex Composite Decentralized Optimization](https://mlsanity.com/paper/2211.11954/) (2022)
- [DIFF2: Differential Private Optimization via Gradient Differences for Nonconvex Distributed Learning](https://mlsanity.com/paper/2302.03884/) (2023)
- [PrivSGP-VR: Differentially Private Variance-Reduced Stochastic Gradient Push with Tight Utility Bounds](https://mlsanity.com/paper/2405.02638/) (2024)
- [A Bias-Correction Decentralized Stochastic Gradient Algorithm with Momentum Acceleration](https://mlsanity.com/paper/2501.19082/) (2025)

## Abstract (arXiv)

Private decentralized learning is affected by sampling noise, privacy noise, and decentralized bias under heterogeneous data. We propose Private Recursive Decentralized Optimization (PRDO). PRDO uses recursive estimation with same-batch gradient differences to reduce estimation errors caused by sampling and privacy noise, while its Exact Diffusion component corrects decentralized bias arising from data heterogeneity. Our analysis establishes a nonconvex convergence bound without assuming uniformly bounded data heterogeneity across nodes. It further gives a sufficient condition under which recursive gradient differences yield strictly lower query sensitivity than private Exact Diffusion, together with an example that rigorously satisfies this condition. Experiments show improved accuracy over the evaluated baselines.