Differentially Private Clipped-SGD: High-Probability Convergence with Arbitrary Clipping Level
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916975629828096 |
|---|---|
| author | Khah, Saleh Vatan Chezhegov, Savelii Farahmand, Shahrokh Horváth, Samuel Gorbunov, Eduard |
| author_facet | Khah, Saleh Vatan Chezhegov, Savelii Farahmand, Shahrokh Horváth, Samuel Gorbunov, Eduard |
| contents | Gradient clipping is a fundamental tool in Deep Learning, improving the high-probability convergence of stochastic first-order methods like SGD, AdaGrad, and Adam under heavy-tailed noise, which is common in training large language models. It is also a crucial component of Differential Privacy (DP) mechanisms. However, existing high-probability convergence analyses typically require the clipping threshold to increase with the number of optimization steps, which is incompatible with standard DP mechanisms like the Gaussian mechanism. In this work, we close this gap by providing the first high-probability convergence analysis for DP-Clipped-SGD with a fixed clipping level, applicable to both convex and non-convex smooth optimization under heavy-tailed noise, characterized by a bounded central $α$-th moment assumption, $α\in (1,2]$. Our results show that, with a fixed clipping level, the method converges to a neighborhood of the optimal solution with a faster rate than the existing ones. The neighborhood can be balanced against the noise introduced by DP, providing a refined trade-off between convergence speed and privacy guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differentially Private Clipped-SGD: High-Probability Convergence with Arbitrary Clipping Level Khah, Saleh Vatan Chezhegov, Savelii Farahmand, Shahrokh Horváth, Samuel Gorbunov, Eduard Machine Learning Optimization and Control Gradient clipping is a fundamental tool in Deep Learning, improving the high-probability convergence of stochastic first-order methods like SGD, AdaGrad, and Adam under heavy-tailed noise, which is common in training large language models. It is also a crucial component of Differential Privacy (DP) mechanisms. However, existing high-probability convergence analyses typically require the clipping threshold to increase with the number of optimization steps, which is incompatible with standard DP mechanisms like the Gaussian mechanism. In this work, we close this gap by providing the first high-probability convergence analysis for DP-Clipped-SGD with a fixed clipping level, applicable to both convex and non-convex smooth optimization under heavy-tailed noise, characterized by a bounded central $α$-th moment assumption, $α\in (1,2]$. Our results show that, with a fixed clipping level, the method converges to a neighborhood of the optimal solution with a faster rate than the existing ones. The neighborhood can be balanced against the noise introduced by DP, providing a refined trade-off between convergence speed and privacy guarantees. |
| title | Differentially Private Clipped-SGD: High-Probability Convergence with Arbitrary Clipping Level |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2507.23512 |