# A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization

arXiv: https://arxiv.org/abs/2509.18134 · HTML: https://mlsanity.com/paper/2509.18134/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 38 references that are in the map.
- First posted on arXiv 14 Sep 2025.

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

- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [EXTRA: An Exact First-Order Algorithm for Decentralized Consensus Optimization](https://mlsanity.com/paper/1404.6264/) (2014)
- [Achieving Geometric Convergence for Distributed Optimization over Time-Varying Graphs](https://mlsanity.com/paper/1607.03218/) (2016)
- [Distributed Stochastic Gradient Tracking Methods](https://mlsanity.com/paper/1805.11454/) (2018)
- [Push-Pull Gradient Methods for Distributed Optimization in Networks](https://mlsanity.com/paper/1810.06653/) (2018)
- [Differentially Private Distributed Optimization](https://mlsanity.com/paper/1401.2596/) (2014)
- [Tailoring Gradient Methods for Differentially-Private Distributed Optimization](https://mlsanity.com/paper/2202.01113/) (2022)
- [Decentralized Stochastic Optimization with Inherent Privacy Protection](https://mlsanity.com/paper/2205.03884/) (2022)
- [Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework](https://mlsanity.com/paper/2004.13999/) (2020)
- [Secure and Privacy-Preserving Consensus](https://mlsanity.com/paper/1707.04491/) (2017)
- [FROST -- Fast row-stochastic optimization with uncoordinated step-sizes](https://mlsanity.com/paper/1803.09169/) (2018)
- [Privacy-Preserving Average Consensus via State Decomposition](https://mlsanity.com/paper/1902.09576/) (2019)
- [A Robust Gradient Tracking Method for Distributed Optimization over Directed Networks](https://mlsanity.com/paper/2003.13980/) (2020)
- [Decentralized Gradient Methods with Time-varying Uncoordinated Stepsizes: Convergence Analysis and Privacy Design](https://mlsanity.com/paper/2205.10934/) (2022)
- [Dynamics based Privacy Preservation in Decentralized Optimization](https://mlsanity.com/paper/2207.05350/) (2022)
- [AB/Push-Pull Method for Distributed Optimization in Time-Varying Directed Networks](https://mlsanity.com/paper/2209.06974/) (2022)
- [Gradient-tracking Based Differentially Private Distributed Optimization with Enhanced Optimization Accuracy](https://mlsanity.com/paper/2212.05364/) (2022)
- [Harnessing Smoothness to Accelerate Distributed Optimization](https://mlsanity.com/paper/1605.07112/) (2016)
- [Differentially Private Average Consensus with Improved Accuracy-Privacy Trade-off](https://mlsanity.com/paper/2309.08464/) (2023)
- [Convergence Rate of Accelerated Average Consensus with Local Node Memory: Optimization and Analytic Solutions](https://mlsanity.com/paper/2110.09678/) (2021)
- [Privacy-Preserving Push-Pull Method for Decentralized Optimization via State Decomposition](https://mlsanity.com/paper/2308.08164/) (2023)
- [Distributed event-triggered aggregative optimization with applications to price-based energy management](https://mlsanity.com/paper/2309.13845/) (2023)
- [Privacy in Multi-agent Systems](https://mlsanity.com/paper/2403.02631/) (2024)
- [Cryptography-Based Privacy-Preserving Method for Distributed Optimization over Time-Varying Directed Graphs with Enhanced Efficiency](https://mlsanity.com/paper/2405.08518/) (2024)

## Abstract (arXiv)

This paper investigates the privacy-preserving distributed optimization problem, aiming to protect agents' private information from potential attackers during the optimization process. Gradient tracking, an advanced technique for improving the convergence rate in distributed optimization, has been applied to most first-order algorithms in recent years. We first reveal the inherent privacy leakage risk associated with gradient tracking. Building upon this insight, we propose a weighted gradient tracking distributed privacy-preserving algorithm, eliminating the privacy leakage risk in gradient tracking using decaying weight factors. Then, we characterize the convergence of the proposed algorithm under time-varying heterogeneous step sizes. We prove the proposed algorithm converges precisely to the optimal solution under mild assumptions. Finally, numerical simulations validate the algorithm's effectiveness through a classical distributed estimation problem and the distributed training of a convolutional neural network.