Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916162379448320 |
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| author | Wang, Jimin Zhang, Ji-Feng |
| author_facet | Wang, Jimin Zhang, Ji-Feng |
| contents | Differentially private distributed stochastic optimization has become a hot topic due to the urgent need of privacy protection in distributed stochastic optimization. In this paper, two-time scale stochastic approximation-type algorithms for differentially private distributed stochastic optimization with time-varying sample sizes are proposed using gradient- and output-perturbation methods. For both gradient- and output-perturbation cases, the convergence of the algorithm and differential privacy with a finite cumulative privacy budget $\varepsilon$ for an infinite number of iterations are simultaneously established, which is substantially different from the existing works. By a time-varying sample sizes method, the privacy level is enhanced, and differential privacy with a finite cumulative privacy budget $\varepsilon$ for an infinite number of iterations is established. By properly choosing a Lyapunov function, the algorithm achieves almost-sure and mean-square convergence even when the added privacy noises have an increasing variance. Furthermore, we rigorously provide the mean-square convergence rates of the algorithm and show how the added privacy noise affects the convergence rate of the algorithm. Finally, numerical examples including distributed training on a benchmark machine learning dataset are presented to demonstrate the efficiency and advantages of the algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11892 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes Wang, Jimin Zhang, Ji-Feng Systems and Control Differentially private distributed stochastic optimization has become a hot topic due to the urgent need of privacy protection in distributed stochastic optimization. In this paper, two-time scale stochastic approximation-type algorithms for differentially private distributed stochastic optimization with time-varying sample sizes are proposed using gradient- and output-perturbation methods. For both gradient- and output-perturbation cases, the convergence of the algorithm and differential privacy with a finite cumulative privacy budget $\varepsilon$ for an infinite number of iterations are simultaneously established, which is substantially different from the existing works. By a time-varying sample sizes method, the privacy level is enhanced, and differential privacy with a finite cumulative privacy budget $\varepsilon$ for an infinite number of iterations is established. By properly choosing a Lyapunov function, the algorithm achieves almost-sure and mean-square convergence even when the added privacy noises have an increasing variance. Furthermore, we rigorously provide the mean-square convergence rates of the algorithm and show how the added privacy noise affects the convergence rate of the algorithm. Finally, numerical examples including distributed training on a benchmark machine learning dataset are presented to demonstrate the efficiency and advantages of the algorithms. |
| title | Differentially Private Distributed Stochastic Optimization with Time-Varying Sample Sizes |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2310.11892 |