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Differentially private stochastic gradient descent (DP-SGD) has become the standard algorithm for training machine learning models with rigorous privacy guarantees. Despite its widespread use, the theoretical understanding of its long-run…

Machine Learning · Computer Science 2025-11-21 Amartya Mukherjee , Jun Liu

Stein Variational Gradient Descent (SVGD) is a widely used sampling algorithm that has been successfully applied in several areas of Machine Learning. SVGD operates by iteratively moving a set of interacting particles (which represent the…

Machine Learning · Computer Science 2024-06-24 Victor Priser , Pascal Bianchi , Adil Salim

Stochastic Gradient Descent (SGD) is a cornerstone of large-scale optimization, yet its theoretical behavior under heavy-tailed noise -- common in modern machine learning and reinforcement learning -- remains poorly understood. In this…

Optimization and Control · Mathematics 2025-08-08 Ilyas Fatkhullin , Florian Hübler , Guanghui Lan

Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. In practice, we notice that the kernel used in SVGD-based methods has a decisive effect on the…

Machine Learning · Computer Science 2022-11-29 Qingzhong Ai , Shiyu Liu , Lirong He , Zenglin Xu

Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…

Optimization and Control · Mathematics 2025-07-01 Måns Williamson , Tony Stillfjord

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…

Machine Learning · Computer Science 2025-04-18 Ruinan Jin , Difei Cheng , Hong Qiao , Xin Shi , Shaodong Liu , Bo Zhang

We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the…

Statistics Theory · Mathematics 2025-06-10 Sayan Banerjee , Krishnakumar Balasubramanian , Promit Ghosal

Gradient clipping is a standard training technique used in deep learning applications such as large-scale language modeling to mitigate exploding gradients. Recent experimental studies have demonstrated a fairly special behavior in the…

Machine Learning · Computer Science 2023-06-06 Amirhossein Reisizadeh , Haochuan Li , Subhro Das , Ali Jadbabaie

Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…

Machine Learning · Statistics 2020-07-29 Xiaoyu Li , Francesco Orabona

Stochastic gradient descent (SGD) algorithm is the method of choice in many machine learning tasks thanks to its scalability and efficiency in dealing with large-scale problems. In this paper, we focus on the shuffling version of SGD which…

Machine Learning · Computer Science 2023-10-27 Lam M. Nguyen , Trang H. Tran

In this paper, we propose a simple variant of the original SVRG, called variance reduced stochastic gradient descent (VR-SGD). Unlike the choices of snapshot and starting points in SVRG and its proximal variant, Prox-SVRG, the two vectors…

Machine Learning · Computer Science 2018-10-31 Fanhua Shang , Kaiwen Zhou , Hongying Liu , James Cheng , Ivor W. Tsang , Lijun Zhang , Dacheng Tao , Licheng Jiao

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…

Machine Learning · Statistics 2018-03-06 Wenqing Hu , Chris Junchi Li , Lei Li , Jian-Guo Liu

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

Numerical Analysis · Mathematics 2017-03-02 Deanna Needell , Rachel Ward

We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a…

Machine Learning · Statistics 2022-05-24 Wei Deng , Guang Lin , Faming Liang

Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…

Optimization and Control · Mathematics 2021-04-02 Vivak Patel , Shushu Zhang

$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…

Optimization and Control · Mathematics 2025-08-13 Zhanhong Jiang , Aditya Balu , Soumik Sarkar

In distributed training of deep neural networks, people usually run Stochastic Gradient Descent (SGD) or its variants on each machine and communicate with other machines periodically. However, SGD might converge slowly in training some deep…

Machine Learning · Computer Science 2022-10-14 Mingrui Liu , Zhenxun Zhuang , Yunwei Lei , Chunyang Liao

Recent empirical evidence indicates that many machine learning applications involve heavy-tailed gradient noise, which challenges the standard assumptions of bounded variance in stochastic optimization. Gradient clipping has emerged as a…

Optimization and Control · Mathematics 2025-07-10 Florian Hübler , Ilyas Fatkhullin , Niao He

The curse of dimensionality is a longstanding challenge in Bayesian inference in high dimensions. In this work, we propose a projected Stein variational gradient descent (pSVGD) method to overcome this challenge by exploiting the…

Machine Learning · Computer Science 2020-06-11 Peng Chen , Omar Ghattas

Approximate Bayesian inference estimates descriptors of an intractable target distribution - in essence, an optimization problem within a family of distributions. For example, Langevin dynamics (LD) extracts asymptotically exact samples…

Machine Learning · Statistics 2021-10-11 Zheyang Shen , Markus Heinonen , Samuel Kaski