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With the increasing practicality of deep learning applications, practitioners are inevitably faced with datasets corrupted by noise from various sources such as measurement errors, mislabeling, and estimated surrogate inputs/outputs that…

Machine Learning · Computer Science 2023-08-30 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Takamitsu Matsubara

Stochastic gradient decent~(SGD) and its variants, including some accelerated variants, have become popular for training in machine learning. However, in all existing SGD and its variants, the sample size in each iteration~(epoch) of…

Machine Learning · Statistics 2019-09-18 Shen-Yi Zhao , Hao Gao , Wu-Jun Li

In this paper, we consider supervised learning problems such as logistic regression and study the stochastic gradient method with averaging, in the usual stochastic approximation setting where observations are used only once. We show that…

Statistics Theory · Mathematics 2014-03-18 Francis Bach

In current deep learning tasks, Adam style optimizers such as Adam, Adagrad, RMSProp, Adafactor, and Lion have been widely used as alternatives to SGD style optimizers. These optimizers typically update model parameters using the sign of…

Machine Learning · Computer Science 2024-10-29 Shuaipeng Li , Penghao Zhao , Hailin Zhang , Xingwu Sun , Hao Wu , Dian Jiao , Weiyan Wang , Chengjun Liu , Zheng Fang , Jinbao Xue , Yangyu Tao , Bin Cui , Di Wang

Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate,…

Machine Learning · Statistics 2016-03-23 Vatsal Shah , Megasthenis Asteris , Anastasios Kyrillidis , Sujay Sanghavi

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of…

Machine Learning · Computer Science 2019-12-16 Andrew Jacobsen , Matthew Schlegel , Cameron Linke , Thomas Degris , Adam White , Martha White

We investigate the dynamical and convergent properties of stochastic gradient descent (SGD) applied to Deep Neural Networks (DNNs). Characterizing the relation between learning rate, batch size and the properties of the final minima, such…

Machine Learning · Computer Science 2018-09-14 Stanisław Jastrzębski , Zachary Kenton , Devansh Arpit , Nicolas Ballas , Asja Fischer , Yoshua Bengio , Amos Storkey

Reinforcement Learning (RL) for training Large Language Models is notoriously unstable. While recent studies attribute this to "training inference mismatch stemming" from inconsistent hybrid engines, standard remedies, such as Importance…

Machine Learning · Computer Science 2026-02-03 Yaxiang Zhang , Yingru Li , Jiacai Liu , Jiawei Xu , Ziniu Li , Qian Liu , Haoyuan Li

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

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 explores two recent methods for learning rate optimisation in stochastic gradient descent: D-Adaptation (arXiv:2301.07733) and probabilistic line search (arXiv:1502.02846). These approaches aim to alleviate the burden of…

Machine Learning · Computer Science 2023-08-08 Max McGuinness

We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the…

Machine Learning · Computer Science 2019-03-26 Giulia Denevi , Carlo Ciliberto , Riccardo Grazzi , Massimiliano Pontil

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Machine Learning · Computer Science 2025-02-12 Son Nguyen , Bo Liu , Lizhang Chen , Qiang Liu

Most optimizers including stochastic gradient descent (SGD) and its adaptive gradient derivatives face the same problem where an effective learning rate during the training is vastly different. A learning rate scheduling, mostly tuned by…

Machine Learning · Computer Science 2019-12-30 Konpat Preechakul , Boonserm Kijsirikul

The performance of stochastic gradient descent (SGD), which is the simplest first-order optimizer for training deep neural networks, depends on not only the learning rate but also the batch size. They both affect the number of iterations…

Machine Learning · Statistics 2024-02-26 Kento Imaizumi , Hideaki Iiduka

We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…

Machine Learning · Statistics 2018-11-19 Patrick Chao , Tahereh Mazaheri , Bo Sun , Nicholas B. Weingartner , Zohar Nussinov

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…

Machine Learning · Computer Science 2019-09-12 Qianqian Tong , Guannan Liang , Jinbo Bi

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

Machine Learning · Computer Science 2016-03-16 Guillaume Bouchard , Théo Trouillon , Julien Perez , Adrien Gaidon

Many popular adaptive gradient methods such as Adam and RMSProp rely on an exponential moving average (EMA) to normalize their stepsizes. While the EMA makes these methods highly responsive to new gradient information, recent research has…

Machine Learning · Computer Science 2021-10-13 Brett Daley , Christopher Amato

For many machine learning problems, data is abundant and it may be prohibitive to make multiple passes through the full training set. In this context, we investigate strategies for dynamically increasing the effective sample size, when…

Machine Learning · Computer Science 2016-10-10 Hadi Daneshmand , Aurelien Lucchi , Thomas Hofmann