# Gradient-tracking Based Differentially Private Distributed Optimization with Enhanced Optimization Accuracy

arXiv: https://arxiv.org/abs/2212.05364 · HTML: https://mlsanity.com/paper/2212.05364/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2022.

## Built on by (most cited first, 5 of 5)

- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Privacy-Preserving Distributed Optimization and Learning](https://mlsanity.com/paper/2403.00157/) (2024)
- [Generalizing Differentially Private Decentralized Deep Learning with Multi-Agent Consensus](https://mlsanity.com/paper/2306.13892/) (2023)
- [Distributed optimization: designed for federated learning](https://mlsanity.com/paper/2508.08606/) (2025)
- [A Weighted Gradient Tracking Privacy-Preserving Method for Distributed Optimization](https://mlsanity.com/paper/2509.18134/) (2025)

## Abstract (arXiv)

Privacy protection has become an increasingly pressing requirement in distributed optimization. However, equipping distributed optimization with differential privacy, the state-of-the-art privacy protection mechanism, will unavoidably compromise optimization accuracy. In this paper, we propose an algorithm to achieve rigorous ε-differential privacy in gradient-tracking based distributed optimization with enhanced optimization accuracy. More specifically, to suppress the influence of differential-privacy noise, we propose a new robust gradient-tracking based distributed optimization algorithm that allows both stepsize and the variance of injected noise to vary with time. Then, we establish a new analyzing approach that can characterize the convergence of the gradient-tracking based algorithm under both constant and time-varying stespsizes. To our knowledge, this is the first analyzing framework that can treat gradient-tracking based distributed optimization under both constant and time-varying stepsizes in a unified manner. More importantly, the new analyzing approach gives a much less conservative analytical bound on the stepsize compared with existing proof techniques for gradient-tracking based distributed optimization. We also theoretically characterize the influence of differential-privacy design on the accuracy of distributed optimization, which reveals that inter-agent interaction has a significant impact on the final optimization accuracy. Numerical simulation results confirm the theoretical predictions.