Learning with Differentially Private Sliced Wasserstein Gradients

D. Rodriguez, C. Lalanne, J. Loubes

In this work, we introduce a novel framework for privately optimizing objectives that depend on sliced Wasserstein distances between data-dependent empirical measures. Our main theoretical contribution is a non-trivial analysis of the sensitivity of the Wasserstein gradients to individual data points, derived from an explicit formulation of the gradient in a fully discrete setting. This enables strong privacy guarantees with minimal utility loss. We demonstrate that standard privacy accounting methods naturally extend to Wasserstein-based objectives, allowing for large-scale private training. This supports a wide range of private machine learning applications involving distribution matching under privacy constraints on the source, the target, or both. These include: (i) an in-processing method for fairness mitigation using a private Wasserstein penalty, and (ii) what we believe is the first approach for training private sliced Wasserstein autoencoders.

Keywords: optimal transport, sliced Wasserstein distance, differential privacy

Machine Learning
September 2, 2026  12:40 PM
Aula 22

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