Pré-Publication, Document De Travail Année : 2025

Learning with Differentially Private (Sliced) Wasserstein Gradients

Résumé

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.

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Dates et versions

hal-04923829 , version 1 (31-01-2025)
hal-04923829 , version 2 (19-05-2025)

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  • HAL Id : hal-04923829 , version 1

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David Rodríguez-Vítores, Clément Lalanne, Jean-Michel Loubes. Learning with Differentially Private (Sliced) Wasserstein Gradients. 2025. ⟨hal-04923829v1⟩
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