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Large language models (LLMs) are trained on vast datasets that may contain sensitive information. Differential privacy (DP), the de facto standard for formal privacy guarantees, provides a principled framework for training LLMs with…

Machine Learning · Computer Science 2026-05-26 Enayat Ullah , Sai Aparna Aketi , Devansh Gupta , Huanyu Zhang , Meisam Razaviyayn

Differential Privacy (DP) is becoming central to large-scale training as privacy regulations tighten. We revisit how DP noise interacts with adaptivity in optimization through the lens of stochastic differential equations, providing the…

Stochastic optimization is a pivotal enabler in modern machine learning, producing effective models for various tasks. However, several existing works have shown that model parameters and gradient information are susceptible to privacy…

Machine Learning · Computer Science 2025-09-15 Zhanhong Jiang , Md Zahid Hasan , Nastaran Saadati , Aditya Balu , Chao Liu , Soumik Sarkar

We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically. We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal…

Optimization and Control · Mathematics 2026-05-05 Davide Nobile , Philipp Grohs

Classical differential private DP-SGD implements individual clipping with random subsampling, which forces a mini-batch SGD approach. We provide a general differential private algorithmic framework that goes beyond DP-SGD and allows any…

Machine Learning · Computer Science 2023-07-26 Marten van Dijk , Phuong Ha Nguyen , Toan N. Nguyen , Lam M. Nguyen

Differentially Private Stochastic Gradient Descent (DPSGD) is widely used to protect sensitive data during the training of machine learning models, but its privacy guarantee often comes at a large cost of model performance due to the lack…

Machine Learning · Computer Science 2026-01-16 Hao Liang , Wanrong Zhang , Xinlei He , Kaishun Wu , Hong Xing

Differentially private stochastic gradient descent (DP-SGD) is the gold standard for training machine learning models with formal differential privacy guarantees. Several recent extensions improve its accuracy by introducing correlated…

Machine Learning · Computer Science 2026-05-13 Nikita P. Kalinin , Ryan McKenna , Rasmus Pagh , Christoph H. Lampert

Differentially-private stochastic gradient descent (DP-SGD) is a family of iterative machine learning training algorithms that privatize gradients to generate a sequence of differentially-private (DP) model parameters. It is also the…

Machine Learning · Computer Science 2025-02-11 Weiwei Kong , Mónica Ribero

Most prior results on differentially private stochastic gradient descent (DP-SGD) are derived under the simplistic assumption of uniform Lipschitzness, i.e., the per-sample gradients are uniformly bounded. We generalize uniform…

Machine Learning · Computer Science 2023-06-07 Rudrajit Das , Satyen Kale , Zheng Xu , Tong Zhang , Sujay Sanghavi

We revisit the problem of linear regression under a differential privacy constraint. By consolidating existing pieces in the literature, we clarify the correct dependence of the feature, label and coefficient domains in the optimization…

Machine Learning · Statistics 2018-07-10 Yu-Xiang Wang

Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Machine Learning · Statistics 2022-10-07 Saad Mohamad , Hamad Alamri , Abdelhamid Bouchachia

Differentially private stochastic gradient descent (DP-SGD) adds noise to gradients in back-propagation, safeguarding training data from privacy leakage, particularly membership inference. It fails to cover (inference-time) threats like…

Cryptography and Security · Computer Science 2023-09-20 Minxin Du , Xiang Yue , Sherman S. M. Chow , Tianhao Wang , Chenyu Huang , Huan Sun

Differential privacy (DP) is a rigorous notion of data privacy, used for private statistics. The canonical algorithm for differentially private mean estimation is to first clip the samples to a bounded range and then add noise to their…

Statistics Theory · Mathematics 2024-10-10 Gautam Kamath , Argyris Mouzakis , Matthew Regehr , Vikrant Singhal , Thomas Steinke , Jonathan Ullman

Learning often involves sensitive data and as such, privacy preserving extensions to Stochastic Gradient Descent (SGD) and other machine learning algorithms have been developed using the definitions of Differential Privacy (DP). In…

Machine Learning · Computer Science 2021-10-14 Friedrich Dörmann , Osvald Frisk , Lars Nørvang Andersen , Christian Fischer Pedersen

We study the learning dynamics of a multi-pass, mini-batch Stochastic Gradient Descent (SGD) procedure for empirical risk minimization in high-dimensional multi-index models with isotropic random data. In an asymptotic regime where the…

Machine Learning · Statistics 2026-02-19 Zhou Fan , Leda Wang

We systematically study the calibration of classifiers trained with differentially private stochastic gradient descent (DP-SGD) and observe miscalibration across a wide range of vision and language tasks. Our analysis identifies per-example…

Machine Learning · Computer Science 2022-11-16 Hanlin Zhang , Xuechen Li , Prithviraj Sen , Salim Roukos , Tatsunori Hashimoto

When applied to large-scale learning problems, the conventional wisdom on privacy-preserving deep learning, known as Differential Private Stochastic Gradient Descent (DP-SGD), has met with limited success due to significant performance…

Machine Learning · Computer Science 2021-12-30 Jian Du , Haitao Mi

This paper presents a parametric solution to piecewise linear regression through the Adaptive Block Gradient Descent (ABGD) algorithm. The heart of the method is the parametrization of piecewise linear functions as the difference of…

Machine Learning · Statistics 2026-05-11 Haitham Kanj , Kiryung Lee

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

Machine Learning · Computer Science 2016-03-16 Guillaume Bouchard , Théo Trouillon , Julien Perez , Adrien Gaidon

Differentially Private Stochastic Gradient Descent (DPSGD) is widely utilized to preserve training data privacy in deep learning, which first clips the gradients to a predefined norm and then injects calibrated noise into the training…

Machine Learning · Computer Science 2024-05-29 Haichao Sha , Yang Cao , Yong Liu , Yuncheng Wu , Ruixuan Liu , Hong Chen