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Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

机器学习 · 计算机科学 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

Compositionality is a basic structural feature of both biological and artificial neural networks. Learning compositional functions via gradient descent incurs well known problems like vanishing and exploding gradients, making careful…

神经与进化计算 · 计算机科学 2021-01-11 Jeremy Bernstein , Jiawei Zhao , Markus Meister , Ming-Yu Liu , Anima Anandkumar , Yisong Yue

We propose a new gradient descent algorithm with added stochastic terms for finding the global optimizers of nonconvex optimization problems. A key component in the algorithm is the adaptive tuning of the randomness based on the value of…

最优化与控制 · 数学 2025-06-16 Björn Engquist , Kui Ren , Yunan Yang

Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable…

最优化与控制 · 数学 2024-02-09 Arnulf Jentzen , Adrian Riekert

In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…

机器学习 · 计算机科学 2026-04-28 Jinhui Bai , Andreas Christmann , Lei Shi

This work is a part of ICLR Reproducibility Challenge 2019, we try to reproduce the results in the conference submission PADAM: Closing The Generalization Gap of Adaptive Gradient Methods In Training Deep Neural Networks. Adaptive gradient…

机器学习 · 计算机科学 2019-01-29 Harshal Mittal , Kartikey Pandey , Yash Kant

Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control…

机器学习 · 计算机科学 2020-10-22 Jie Liu , Chen Lin , Chuming Li , Lu Sheng , Ming Sun , Junjie Yan , Wanli Ouyang

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…

最优化与控制 · 数学 2025-07-01 Måns Williamson , Tony Stillfjord

In this work, we question the necessity of adaptive gradient methods for training deep neural networks. SGD-SaI is a simple yet effective enhancement to stochastic gradient descent with momentum (SGDM). SGD-SaI performs learning rate…

机器学习 · 计算机科学 2024-12-18 Minghao Xu , Lichuan Xiang , Xu Cai , Hongkai Wen

First-order optimization algorithms have been proven prominent in deep learning. In particular, algorithms such as RMSProp and Adam are extremely popular. However, recent works have pointed out the lack of ``long-term memory" in Adam-like…

机器学习 · 计算机科学 2020-12-01 Haiwen Huang , Chang Wang , Bin Dong

How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…

计算机视觉与模式识别 · 计算机科学 2020-11-17 Zhaoqun Li

Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…

机器学习 · 计算机科学 2023-12-19 Persia Jana Kamali , Pierfrancesco Urbani

To fully uncover the great potential of deep neural networks (DNNs), various learning algorithms have been developed to improve the model's generalization ability. Recently, sharpness-aware minimization (SAM) establishes a generic scheme…

计算机视觉与模式识别 · 计算机科学 2022-11-22 Tao Li , Weihao Yan , Zehao Lei , Yingwen Wu , Kun Fang , Ming Yang , Xiaolin Huang

Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods have seen a recent resurgence, demonstrating impressive…

机器学习 · 计算机科学 2025-02-05 Thomas T. Zhang , Behrad Moniri , Ansh Nagwekar , Faraz Rahman , Anton Xue , Hamed Hassani , Nikolai Matni

Regularization is a critical component in deep learning. The most commonly used approach, weight decay, applies a constant penalty coefficient uniformly across all parameters. This may be overly restrictive for some parameters, while…

机器学习 · 计算机科学 2024-12-10 Jörg K. H. Franke , Michael Hefenbrock , Gregor Koehler , Frank Hutter

We present a novel universal gradient method for solving convex optimization problems. Our algorithm, Dual Averaging with Distance Adaptation (DADA), is based on the classical scheme of dual averaging and dynamically adjusts its…

最优化与控制 · 数学 2026-04-22 Mohammad Moshtaghifar , Anton Rodomanov , Daniil Vankov , Sebastian Stich

Recent work [4] analyses the local convergence of Adam in a neighbourhood of an optimal solution for a twice-differentiable function. It is found that the learning rate has to be sufficiently small to ensure local stability of the optimal…

机器学习 · 计算机科学 2021-12-14 Guoqiang Zhang , Niwa Kenta , W. Bastiaan Kleijn

Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…

最优化与控制 · 数学 2025-05-28 Tuo Liu , El Mehdi Saad , Wojciech Kotłowski , Francesco Orabona

Reinforcement learning (RL), particularly RL from verifiable reward (RLVR), has become a crucial phase of training large language models (LLMs) and a key focus of current scaling efforts. However, optimization practices in RL largely follow…

机器学习 · 计算机科学 2026-02-25 Sagnik Mukherjee , Lifan Yuan , Pavan Jayasinha , Dilek Hakkani-Tür , Hao Peng

Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…

最优化与控制 · 数学 2020-10-20 Thinh T. Doan , Lam M. Nguyen , Nhan H. Pham , Justin Romberg