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The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…

Machine Learning · Computer Science 2025-06-13 Liu Ziyin , Hongchao Li , Masahito Ueda

Large-scale distributed optimization is of great importance in various applications. For data-parallel based distributed learning, the inter-node gradient communication often becomes the performance bottleneck. In this paper, we propose the…

Computer Vision and Pattern Recognition · Computer Science 2018-06-22 Jiaxiang Wu , Weidong Huang , Junzhou Huang , Tong Zhang

Boosting algorithms to simultaneously estimate and select predictor effects in statistical models have gained substantial interest during the last decade. This review article aims to highlight recent methodological developments regarding…

Methodology · Statistics 2014-11-19 Andreas Mayr , Harald Binder , Olaf Gefeller , Matthias Schmid

Stochastic Gradient Descent (SGD) and its momentum variants form the backbone of deep learning optimization, yet the underlying dynamics of their gradient behavior remain insufficiently understood. In this work, we reinterpret gradient…

Machine Learning · Computer Science 2026-03-09 Zhipeng Yao , Rui Yu , Guisong Chang , Ying Li , Yu Zhang , Dazhou Li

In this paper, we investigate the theoretical properties of stochastic gradient descent (SGD) for statistical inference in the context of nonconvex optimization problems, which have been relatively unexplored compared to convex settings.…

Machine Learning · Statistics 2023-06-06 Yanjie Zhong , Todd Kuffner , Soumendra Lahiri

In this work, we consider the problem of a network of agents collectively minimizing a sum of convex functions. The agents in our setting can only access their local objective functions and exchange information with their immediate…

Optimization and Control · Mathematics 2019-10-01 Charikleia Iakovidou , Ermin Wei

(Mini-batch) Stochastic Gradient Descent is a popular optimization method which has been applied to many machine learning applications. But a rather high variance introduced by the stochastic gradient in each step may slow down the…

Machine Learning · Computer Science 2018-10-09 Jingchang Liu , Linli Xu

We propose a general method called truncated gradient to induce sparsity in the weights of online learning algorithms with convex loss functions. This method has several essential properties: The degree of sparsity is continuous -- a…

Machine Learning · Computer Science 2008-07-04 John Langford , Lihong Li , Tong Zhang

Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this paper, we study the dynamics of stochastic gradient descent over diagonal linear…

Machine Learning · Computer Science 2021-12-08 Scott Pesme , Loucas Pillaud-Vivien , Nicolas Flammarion

Gradient-variation online learning aims to achieve regret guarantees that scale with variations in the gradients of online functions, which has been shown to be crucial for attaining fast convergence in games and robustness in stochastic…

Machine Learning · Computer Science 2024-11-05 Yan-Feng Xie , Peng Zhao , Zhi-Hua Zhou

Gradient Boosted Decision Trees (GBDT) is a very successful ensemble learning algorithm widely used across a variety of applications. Recently, several variants of GBDT training algorithms and implementations have been designed and heavily…

Machine Learning · Computer Science 2019-06-27 Yu Shi , Jian Li , Zhize Li

Alongside the well-publicized accomplishments of deep neural networks there has emerged an apparent bug in their success on tasks such as object recognition: with deep models trained using vanilla methods, input images can be slightly…

Machine Learning · Computer Science 2021-03-04 Jacob Abernethy , Pranjal Awasthi , Satyen Kale

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

Boosting combines weak (biased) learners to obtain effective learning algorithms for classification and prediction. In this paper, we show a connection between boosting and kernel-based methods, highlighting both theoretical and practical…

Machine Learning · Statistics 2017-04-14 Aleksandr Y. Aravkin , Giulio Bottegal , Gianluigi Pillonetto

Despite an extensive body of literature on deep learning optimization, our current understanding of what makes an optimization algorithm effective is fragmented. In particular, we do not understand well whether enhanced optimization…

Machine Learning · Computer Science 2024-03-04 Toki Tahmid Inan , Mingrui Liu , Amarda Shehu

Online decision making aims to learn the optimal decision rule by making personalized decisions and updating the decision rule recursively. It has become easier than before with the help of big data, but new challenges also come along.…

Machine Learning · Statistics 2020-10-16 Haoyu Chen , Wenbin Lu , Rui Song

We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models…

Machine Learning · Computer Science 2020-06-11 Tony Duan , Anand Avati , Daisy Yi Ding , Khanh K. Thai , Sanjay Basu , Andrew Y. Ng , Alejandro Schuler

Online nonparametric estimators are gaining popularity due to their efficient computation and competitive generalization abilities. An important example includes variants of stochastic gradient descent. These algorithms often take one…

Statistics Theory · Mathematics 2025-07-08 Tianyu Zhang , Jing Lei

This paper introduces Mixed Effect Gradient Boosting (MEGB), which combines the strengths of Gradient Boosting with Mixed Effects models to address complex, hierarchical data structures often encountered in statistical analysis. The…

Methodology · Statistics 2025-01-22 Paul Messer , Timo Schmid

The success of SGD in deep learning has been ascribed by prior works to the implicit bias induced by finite batch sizes ("SGD noise"). While prior works focused on offline learning (i.e., multiple-epoch training), we study the impact of SGD…

Machine Learning · Computer Science 2024-06-10 Nikhil Vyas , Depen Morwani , Rosie Zhao , Gal Kaplun , Sham Kakade , Boaz Barak