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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…

Optimization and Control · Mathematics 2025-05-28 Tuo Liu , El Mehdi Saad , Wojciech Kotłowski , Francesco Orabona

We introduce a doubly stochastic proximal gradient algorithm for optimizing a finite average of smooth convex functions, whose gradients depend on numerically expensive expectations. Our main motivation is the acceleration of the…

Machine Learning · Statistics 2016-11-09 Massil Achab , Agathe Guilloux , Stéphane Gaïffas , Emmanuel Bacry

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

Machine Learning · Computer Science 2016-01-14 Yadong Mu , Wei Liu , Wei Fan

Recent advances in deep reinforcement learning have achieved human-level performance on a variety of real-world applications. However, the current algorithms still suffer from poor gradient estimation with excessive variance, resulting in…

Machine Learning · Computer Science 2019-05-21 Wei-Ye Zhao , Xi-Ya Guan , Yang Liu , Xiaoming Zhao , Jian Peng

A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…

Machine Learning · Computer Science 2015-09-25 Craig Wilson , Venugopal V. Veeravalli

Conventional learning methods simplify the bilinear model by regarding two intrinsically coupled factors independently, which degrades the optimization procedure. One reason lies in the insufficient training due to the asynchronous gradient…

Computer Vision and Pattern Recognition · Computer Science 2020-06-17 Li'an Zhuo , Baochang Zhang , Linlin Yang , Hanlin Chen , Qixiang Ye , David Doermann , Guodong Guo , Rongrong Ji

Since distribution shifts are common in real-world applications, there is a pressing need to develop prediction models that are robust against such shifts. Existing frameworks, such as empirical risk minimization or distributionally robust…

Methodology · Statistics 2025-03-25 Xinwei Shen , Peter Bühlmann , Armeen Taeb

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…

Optimization and Control · Mathematics 2020-03-31 Bin Hu , Peter Seiler , Laurent Lessard

We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous…

Machine Learning · Statistics 2025-09-09 Naoki Yoshida , Shogo Nakakita , Masaaki Imaizumi

This paper introduces two variational inference approaches for infinite-dimensional inverse problems, developed through gradient descent with a constant learning rate. The proposed methods enable efficient approximate sampling from the…

Numerical Analysis · Mathematics 2026-03-05 Jiaming Sui , Junxiong Jia , Jinglai Li

The learning rate is perhaps the single most important parameter in the training of neural networks and, more broadly, in stochastic (nonconvex) optimization. Accordingly, there are numerous effective, but poorly understood, techniques for…

Machine Learning · Computer Science 2020-04-16 Bin Shi , Weijie J. Su , Michael I. Jordan

Stochastic Gradient Descent (SGD), a widely used optimization algorithm in deep learning, is often limited to converging to local optima due to the non-convex nature of the problem. Leveraging these local optima to improve model performance…

Machine Learning · Computer Science 2023-09-22 Hao Chen , Yusen Wu , Phuong Nguyen , Chao Liu , Yelena Yesha

When training the parameters of a linear dynamical model, the gradient descent algorithm is likely to fail to converge if the squared-error loss is used as the training loss function. Restricting the parameter space to a smaller subset and…

Machine Learning · Computer Science 2020-07-13 Kamil Nar , Yuan Xue , Andrew M. Dai

The minibatch stochastic gradient descent method (SGD) is widely applied in deep learning due to its efficiency and scalability that enable training deep networks with a large volume of data. Particularly in the distributed setting, SGD is…

Machine Learning · Computer Science 2020-11-19 Qiwei Yuan , Weizhe Hua , Yi Zhou , Cunxi Yu

Bias is a common problem inherent in recommender systems, which is entangled with users' preferences and poses a great challenge to unbiased learning. For debiasing tasks, the doubly robust (DR) method and its variants show superior…

Information Retrieval · Computer Science 2023-03-03 Haoxuan Li , Yan Lyu , Chunyuan Zheng , Peng Wu

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we…

Machine Learning · Statistics 2018-08-08 Francois Fagan , Garud Iyengar

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…

Machine Learning · Computer Science 2020-10-22 Jie Liu , Chen Lin , Chuming Li , Lu Sheng , Ming Sun , Junjie Yan , Wanli Ouyang

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

Optimization and Control · Mathematics 2021-06-09 Mert Gürbüzbalaban , Andrzej Ruszczyński , Landi Zhu

Deep reinforcement learning (RL) suffers from plasticity loss severely due to the nature of non-stationarity, which impairs the ability to adapt to new data and learn continually. Unfortunately, our understanding of how plasticity loss…

Machine Learning · Computer Science 2026-04-03 Zihao Wu , Hongyao Tang , Yi Ma , Jiashun Liu , Yan Zheng , Jianye Hao

Stochastic graph neural networks (SGNNs) are information processing architectures that learn representations from data over random graphs. SGNNs are trained with respect to the expected performance, which comes with no guarantee about…

Signal Processing · Electrical Eng. & Systems 2023-03-22 Zhan Gao , Elvin Isufi