GeoClip: Geometry-Aware Clipping for Differentially Private SGD
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912673256439808 |
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| author | Gilani, Atefeh Tasnim, Naima Sankar, Lalitha Kosut, Oliver |
| author_facet | Gilani, Atefeh Tasnim, Naima Sankar, Lalitha Kosut, Oliver |
| contents | Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_06549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GeoClip: Geometry-Aware Clipping for Differentially Private SGD Gilani, Atefeh Tasnim, Naima Sankar, Lalitha Kosut, Oliver Machine Learning Cryptography and Security Information Theory Differentially private stochastic gradient descent (DP-SGD) is the most widely used method for training machine learning models with provable privacy guarantees. A key challenge in DP-SGD is setting the per-sample gradient clipping threshold, which significantly affects the trade-off between privacy and utility. While recent adaptive methods improve performance by adjusting this threshold during training, they operate in the standard coordinate system and fail to account for correlations across the coordinates of the gradient. We propose GeoClip, a geometry-aware framework that clips and perturbs gradients in a transformed basis aligned with the geometry of the gradient distribution. GeoClip adaptively estimates this transformation using only previously released noisy gradients, incurring no additional privacy cost. We provide convergence guarantees for GeoClip and derive a closed-form solution for the optimal transformation that minimizes the amount of noise added while keeping the probability of gradient clipping under control. Experiments on both tabular and image datasets demonstrate that GeoClip consistently outperforms existing adaptive clipping methods under the same privacy budget. |
| title | GeoClip: Geometry-Aware Clipping for Differentially Private SGD |
| topic | Machine Learning Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2506.06549 |