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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.13011 |
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| _version_ | 1866917771961434112 |
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| author | Jin, Chenhan Zhou, Kaiwen Han, Bo Cheng, James Zeng, Tieyong |
| author_facet | Jin, Chenhan Zhou, Kaiwen Han, Bo Cheng, James Zeng, Tieyong |
| contents | We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted to gradient descent (GD) or performed multi-times clipping on stochastic gradient descent (SGD), which is inefficient for large-scale problems. In this paper, we consider a one-time clipping strategy and provide principled analyses of its bias and private mean estimation. We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems. We also extend our convergent analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\ddot{\text{o}}$lder-continuous gradients). All the above results are guaranteed with a high probability for heavy-tailed data. Numerical experiments are conducted to justify the theoretical improvement. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_13011 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Efficient Private SCO for Heavy-Tailed Data via Averaged Clipping Jin, Chenhan Zhou, Kaiwen Han, Bo Cheng, James Zeng, Tieyong Machine Learning Optimization and Control We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Most prior works on differentially private stochastic convex optimization for heavy-tailed data are either restricted to gradient descent (GD) or performed multi-times clipping on stochastic gradient descent (SGD), which is inefficient for large-scale problems. In this paper, we consider a one-time clipping strategy and provide principled analyses of its bias and private mean estimation. We establish new convergence results and improved complexity bounds for the proposed algorithm called AClipped-dpSGD for constrained and unconstrained convex problems. We also extend our convergent analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\ddot{\text{o}}$lder-continuous gradients). All the above results are guaranteed with a high probability for heavy-tailed data. Numerical experiments are conducted to justify the theoretical improvement. |
| title | Efficient Private SCO for Heavy-Tailed Data via Averaged Clipping |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2206.13011 |