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Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an…

Machine Learning · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

The Adam optimizer remains one of the most widely used optimizers in deep learning, and effectively tuning its hyperparameters is key to optimizing performance. However, tuning can be tedious and costly. Freeze-thaw Bayesian Optimization…

Machine Learning · Computer Science 2025-08-29 Theodoros Athanasiadis , Steven Adriaensen , Samuel Müller , Frank Hutter

When training neural models, it is common to combine multiple loss terms. The balancing of these terms requires considerable human effort and is computationally demanding. Moreover, the optimal trade-off between the loss term can change as…

Machine Learning · Computer Science 2020-06-29 Itzik Malkiel , Lior Wolf

Adaptive Moment Estimation (Adam) is a cornerstone optimization algorithm in deep learning, widely recognized for its flexibility with adaptive learning rates and efficiency in handling large-scale data. However, despite its practical…

Machine Learning · Computer Science 2025-05-21 Ruinan Jin , Xiao Li , Yaoliang Yu , Baoxiang Wang

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

Machine Learning · Computer Science 2021-08-26 Difan Zou , Yuan Cao , Yuanzhi Li , Quanquan Gu

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving…

Machine Learning · Computer Science 2019-04-22 Sashank J. Reddi , Satyen Kale , Sanjiv Kumar

The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…

Machine Learning · Computer Science 2021-09-10 Anirudh Maiya , Inumella Sricharan , Anshuman Pandey , Srinivas K. S

Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM…

Optimization and Control · Mathematics 2025-05-29 Arnulf Jentzen , Julian Kranz , Adrian Riekert

Artificial neural networks play a crucial role in machine learning and there is a need to improve their performance. This paper presents FOXANN, a novel classification model that combines the recently developed Fox optimizer with ANN to…

Neural and Evolutionary Computing · Computer Science 2024-07-08 Mahmood A. Jumaah , Yossra H. Ali , Tarik A. Rashid , S. Vimal

Many adaptive optimization methods have been proposed and used in deep learning, in which Adam is regarded as the default algorithm and widely used in many deep learning frameworks. Recently, many variants of Adam, such as Adabound, RAdam…

Machine Learning · Computer Science 2020-11-05 Wei Yuan , Kai-Xin Gao

Adam-type methods, the extension of adaptive gradient methods, have shown great performance in the training of both supervised and unsupervised machine learning models. In particular, Adam-type optimizers have been widely used empirically…

Machine Learning · Computer Science 2021-09-30 Zehao Dou , Yuanzhi Li

Machine learning algorithms aim to find patterns from observations, which may include some noise, especially in robotics domain. To perform well even with such noise, we expect them to be able to detect outliers and discard them when…

Machine Learning · Computer Science 2020-03-04 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Kenji Sugimoto

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

Despite the success of the Adam optimizer in practice, the theoretical understanding of its algorithmic components still remains limited. In particular, most existing analyses of Adam show the convergence rate that can be simply achieved by…

Machine Learning · Computer Science 2024-05-31 Kwangjun Ahn , Zhiyu Zhang , Yunbum Kook , Yan Dai

In recent years, federated minimax optimization has attracted growing interest due to its extensive applications in various machine learning tasks. While Smoothed Alternative Gradient Descent Ascent (Smoothed-AGDA) has proved its success in…

Machine Learning · Statistics 2024-04-22 Wei Shen , Minhui Huang , Jiawei Zhang , Cong Shen

We introduce Velocity-Regularized Adam (VRAdam), a physics-inspired optimizer for training deep neural networks that draws on ideas from quartic terms for kinetic energy with its stabilizing effects on various system dynamics. Previous…

Machine Learning · Computer Science 2026-05-13 Pranav Vaidhyanathan , Lucas Schorling , Natalia Ares , Michael A. Osborne

We present a method to formulate algorithm discovery as program search, and apply it to discover optimization algorithms for deep neural network training. We leverage efficient search techniques to explore an infinite and sparse program…

We study optimization for losses that admit a variance-mean scale-mixture representation. Under this representation, each EM iteration is a weighted least squares update in which latent variables determine observation and parameter weights;…

Computation · Statistics 2026-02-17 Nick Polson , Vadim Sokolov

Beside the standard stochastic gradient descent (SGD) method, the Adam optimizer due to Kingma & Ba (2014) is currently probably the best-known optimization method for the training of deep neural networks in artificial intelligence (AI)…

Optimization and Control · Mathematics 2025-11-11 Steffen Dereich , Thang Do , Arnulf Jentzen , Philippe von Wurstemberger

This work introduces ZetA, a novel deep learning optimizer that extends Adam by incorporating dynamic scaling based on the Riemann zeta function. To the best of our knowledge, ZetA is the first optimizer to apply zeta-based gradient scaling…

Machine Learning · Computer Science 2025-08-06 Samiksha BC