{"ID":2839665,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15634","arxiv_id":"2511.15634","title":"Rényi Differential Privacy for Heavy-Tailed SDEs via Fractional Poincaré Inequalities","abstract":"Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of stochastic gradient descent (SGD) with heavy-tailed noise, both as a model for modern deep learning models and to improve their performance. However, most DP bounds focus on light-tailed noise, where satisfactory guarantees have been obtained but the proposed techniques do not directly extend to the heavy-tailed setting. Recently, the first DP guarantees for heavy-tailed SGD were obtained. These results provide $(0,δ)$-DP guarantees without requiring gradient clipping. Despite casting new light on the link between DP and heavy-tailed algorithms, these results have a strong dependence on the number of parameters and cannot be extended to other DP notions like the well-established Rényi differential privacy (RDP). In this work, we propose to address these limitations by deriving the first RDP guarantees for heavy-tailed SDEs, as well as their discretized counterparts. Our framework is based on new Rényi flow computations and the use of well-established fractional Poincaré inequalities. Under the assumption that such inequalities are satisfied, we obtain DP guarantees that have a much weaker dependence on the dimension compared to prior art.","short_abstract":"Characterizing the differential privacy (DP) of learning algorithms has become a major challenge in recent years. In parallel, many studies suggested investigating the behavior of stochastic gradient descent (SGD) with heavy-tailed noise, both as a model for modern deep learning models and to improve their performance....","url_abs":"https://arxiv.org/abs/2511.15634","url_pdf":"https://arxiv.org/pdf/2511.15634v1","authors":"[\"Benjamin Dupuis\",\"Mert Gürbüzbalaban\",\"Umut Şimşekli\",\"Jian Wang\",\"Sinan Yildirim\",\"Lingjiong Zhu\"]","published":"2025-11-19T17:18:54Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}