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Gradient-based optimization drives the unprecedented performance of modern deep neural network models across diverse applications. Adaptive algorithms have accelerated neural network training due to their rapid convergence rates; however,…

Machine Learning · Computer Science 2025-05-06 Chia-Wei Hsu , Nien-Ti Tsou , Yu-Cheng Chen , Yang Jeong Park , Ju Li

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values…

Machine Learning · Computer Science 2021-01-25 Dariush Bahrami , Sadegh Pouriyan Zadeh

Recent works have shown that gradient-update alignment is a powerful signal for modulating optimizer updates, often leading to faster training. We promote this update-wise heuristic as a mathematically grounded principle for selecting and…

Machine Learning · Computer Science 2026-05-08 Jaerin Lee , Kyoung Mu Lee

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…

Optimization and Control · Mathematics 2022-03-24 Hailiang Liu , Xuping Tian

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

Optimization and Control · Mathematics 2021-01-01 Lihua Lei , Michael I. Jordan

Balancing convergence speed, generalization capability, and computational efficiency remains a core challenge in deep learning optimization. First-order gradient descent methods, epitomized by stochastic gradient descent (SGD) and Adam,…

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

Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…

Machine Learning · Computer Science 2025-11-05 Xinghan Li , Haodong Wen , Kaifeng Lyu

In recent years, deep learning has achieved remarkable success in various fields such as image recognition, natural language processing, and speech recognition. The effectiveness of deep learning largely depends on the optimization methods…

Machine Learning · Computer Science 2023-04-25 David Shulman

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

Machine Learning · Computer Science 2020-12-04 Bao Wang , Qiang Ye

Modern machine learning algorithms usually involve tuning multiple (from one to thousands) hyperparameters which play a pivotal role in terms of model generalizability. Black-box optimization and gradient-based algorithms are two dominant…

Machine Learning · Computer Science 2021-02-19 Bin Gu , Guodong Liu , Yanfu Zhang , Xiang Geng , Heng Huang

Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…

Machine Learning · Computer Science 2021-03-30 Loris Nanni , Gianluca Maguolo , Alessandra Lumini

Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…

Optimization and Control · Mathematics 2025-11-11 Mohammad Sadegh Salehi , Subhadip Mukherjee , Lindon Roberts , Matthias J. Ehrhardt

The vast majority of modern deep learning models are trained with momentum-based first-order optimizers. The momentum term governs the optimizer's memory by determining how much each past gradient contributes to the current convergence…

Machine Learning · Computer Science 2026-05-12 Kristi Topollai , Anna Choromanska

Tuning hyperparameters, such as the stepsize, presents a major challenge of training machine learning models. To address this challenge, numerous adaptive optimization algorithms have been developed that achieve near-optimal complexities,…

Optimization and Control · Mathematics 2023-11-07 Florian Hübler , Junchi Yang , Xiang Li , Niao He

We introduce LDAdam, a memory-efficient optimizer for training large models, that performs adaptive optimization steps within lower dimensional subspaces, while consistently exploring the full parameter space during training. This strategy…

Machine Learning · Computer Science 2025-03-04 Thomas Robert , Mher Safaryan , Ionut-Vlad Modoranu , Dan Alistarh

The choices of hyperparameters have critical effects on the performance of machine learning models. In this paper, we present a general framework that is able to construct an adaptive optimizer, which automatically adjust the appropriate…

Machine Learning · Computer Science 2022-01-31 Huayuan Sun

Optimal selection of optimization algorithms is crucial for training deep learning models. The Adam optimizer has gained significant attention due to its efficiency and wide applicability. However, to enhance the adaptability of optimizers…

Machine Learning · Computer Science 2024-09-09 Chengxi Pan , Junshang Chen , Jingrui Ye

Machine learning algorithms have been used widely in various applications and areas. To fit a machine learning model into different problems, its hyper-parameters must be tuned. Selecting the best hyper-parameter configuration for machine…

Machine Learning · Computer Science 2022-10-06 Li Yang , Abdallah Shami

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters…