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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

We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient…

Machine Learning · Computer Science 2016-05-25 Jianhui Chen , Tianbao Yang , Qihang Lin , Lijun Zhang , Yi Chang

With the assistance of singular value decomposition (SVD), a multi-beam directional modulation (DM) scheme based on symmetrical multi-carrier frequency diverse array (FDA) is proposed. The proposed DM scheme is capable of achieving…

Signal Processing · Electrical Eng. & Systems 2019-07-30 Qian Cheng , Vincent Fusco , Jiang Zhu , Shilian Wang , Chao Gu

Sparsity regularized loss minimization problems play an important role in various fields including machine learning, data mining, and modern statistics. Proximal gradient descent method and coordinate descent method are the most popular…

Machine Learning · Computer Science 2023-11-13 Runxue Bao , Bin Gu , Heng Huang

The focus of this paper is on spatial precoding in correlated multi-antenna channels, where the number of independent data-streams is adapted to trade-off the data-rate with the transmitter complexity. Towards the goal of a low-complexity…

Information Theory · Computer Science 2009-09-29 Vasanthan Raghavan , Akbar Sayeed , Venu Veeravalli

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

We study private stochastic convex optimization (SCO) under user-level differential privacy (DP) constraints. In this setting, there are $n$ users (e.g., cell phones), each possessing $m$ data items (e.g., text messages), and we need to…

Machine Learning · Computer Science 2024-10-25 Andrew Lowy , Daogao Liu , Hilal Asi

Differentially private (DP) stochastic convex optimization (SCO) is a fundamental problem, where the goal is to approximately minimize the population risk with respect to a convex loss function, given a dataset of $n$ i.i.d. samples from a…

Machine Learning · Computer Science 2022-05-06 Raef Bassily , Cristóbal Guzmán , Anupama Nandi

This paper presents a holistic approach to gradient leakage resilient distributed Stochastic Gradient Descent (SGD). First, we analyze two types of strategies for privacy-enhanced federated learning: (i) gradient pruning with random…

Machine Learning · Computer Science 2023-05-12 Wenqi Wei , Ling Liu , Jingya Zhou , Ka-Ho Chow , Yanzhao Wu

Machine learning (ML) models trained by differentially private stochastic gradient descent (DP-SGD) have much lower utility than the non-private ones. To mitigate this degradation, we propose a DP Laplacian smoothing SGD (DP-LSSGD) to train…

Machine Learning · Computer Science 2019-12-10 Bao Wang , Quanquan Gu , March Boedihardjo , Farzin Barekat , Stanley J. Osher

This paper considers coordinated linear precoding in downlink multicell multiuser orthogonal frequency-division multiple access (OFDMA) network. A less-complex, fast and provably convergent algorithm that maximizes the weighted sum-rate…

Information Theory · Computer Science 2017-08-17 Mirza Golam Kibria , Hidekazu Murata , Susumu Yoshida

Stochastic Gradient Descent (SGD) often slows in the late stage of training due to anisotropic curvature and gradient noise. We analyze preconditioned SGD in the geometry induced by a symmetric positive definite matrix $\mathbf{M}$,…

Numerical Analysis · Mathematics 2025-11-26 Mitchell Scott , Tianshi Xu , Ziyuan Tang , Alexandra Pichette-Emmons , Qiang Ye , Yousef Saad , Yuanzhe Xi

In this paper, we investigate the downlink transmission of a multiuser multiple-input single-output (MISO) channel under a symbol-level precoding (SLP) scheme, having imperfect channel knowledge at the transmitter. In defining the SLP…

Signal Processing · Electrical Eng. & Systems 2018-08-14 Alireza Haqiqatnejad , Farbod Kayhan , Bjorn Ottersten

The robustness of a neural network to adversarial examples can be provably certified by solving a convex relaxation. If the relaxation is loose, however, then the resulting certificate can be too conservative to be practically useful.…

Optimization and Control · Mathematics 2020-10-28 Richard Y. Zhang

This paper proposes a new large-scale mask-compliant spectral precoder (LS-MSP) for orthogonal frequency division multiplexing systems. In this paper, we first consider a previously proposed mask-compliant spectral precoding scheme that…

Signal Processing · Electrical Eng. & Systems 2019-05-17 Shashi Kant , Gabor Fodor , Mats Bengtsson , Bo Göransson , Carlo Fischione

We consider the problem of minimizing a convex risk with stochastic subgradients guaranteeing $\epsilon$-locally differentially private ($\epsilon$-LDP). While it has been shown that stochastic optimization is possible with $\epsilon$-LDP…

Machine Learning · Computer Science 2019-11-22 Kwang-Sung Jun , Francesco Orabona

A succinct histogram captures frequent items and their frequencies across clients and has become increasingly important for large-scale, privacy-sensitive machine learning applications. To develop a rigorous framework to guarantee privacy…

Cryptography and Security · Computer Science 2025-06-24 Hsuan-Po Liu , Hessam Mahdavifar

While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…

Optimization and Control · Mathematics 2018-02-19 Peng Xu , Farbod Roosta-Khorasani , Michael W. Mahoney

Low-resolution precoding techniques have gained considerable attention in the wireless communications area recently. Vital but hardly discussed in literature, discrete precoding in conjunction with channel coding is the subject of this…

Information Theory · Computer Science 2021-05-21 Erico S. P. Lopes , Lukas T. N. Landau

Differentially private stochastic gradient descent (DP-SGD) is broadly considered to be the gold standard for training and fine-tuning neural networks under differential privacy (DP). With the increasing availability of high-quality…

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