Learning with Differentially Private (Sliced) Wasserstein Gradients
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909618447319040 |
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| author | Rodríguez-Vítores, David Lalanne, Clément Loubes, Jean-Michel |
| author_facet | Rodríguez-Vítores, David Lalanne, Clément Loubes, Jean-Michel |
| contents | In this work, we introduce a novel framework for privately optimizing objectives that rely on Wasserstein distances between data-dependent empirical measures. Our main theoretical contribution is, based on an explicit formulation of the Wasserstein gradient in a fully discrete setting, a control on the sensitivity of this gradient to individual data points, allowing strong privacy guarantees at minimal utility cost. Building on these insights, we develop a deep learning approach that incorporates gradient and activations clipping, originally designed for DP training of problems with a finite-sum structure. We further demonstrate that privacy accounting methods extend to Wasserstein-based objectives, facilitating large-scale private training. Empirical results confirm that our framework effectively balances accuracy and privacy, offering a theoretically sound solution for privacy-preserving machine learning tasks relying on optimal transport distances such as Wasserstein distance or sliced-Wasserstein distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01701 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning with Differentially Private (Sliced) Wasserstein Gradients Rodríguez-Vítores, David Lalanne, Clément Loubes, Jean-Michel Machine Learning Artificial Intelligence Statistics Theory In this work, we introduce a novel framework for privately optimizing objectives that rely on Wasserstein distances between data-dependent empirical measures. Our main theoretical contribution is, based on an explicit formulation of the Wasserstein gradient in a fully discrete setting, a control on the sensitivity of this gradient to individual data points, allowing strong privacy guarantees at minimal utility cost. Building on these insights, we develop a deep learning approach that incorporates gradient and activations clipping, originally designed for DP training of problems with a finite-sum structure. We further demonstrate that privacy accounting methods extend to Wasserstein-based objectives, facilitating large-scale private training. Empirical results confirm that our framework effectively balances accuracy and privacy, offering a theoretically sound solution for privacy-preserving machine learning tasks relying on optimal transport distances such as Wasserstein distance or sliced-Wasserstein distance. |
| title | Learning with Differentially Private (Sliced) Wasserstein Gradients |
| topic | Machine Learning Artificial Intelligence Statistics Theory |
| url | https://arxiv.org/abs/2502.01701 |