2025/02/03 by David Rodríguez-Vítores, Rodríguez-Vítores, David, Lalanne, Clément +1
Computer Science · #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Privacy-Preserving Technologies in Data #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2502.01701
openalex publication_date 2025/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.