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Related papers: Adam: A Method for Stochastic Optimization

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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

In this work, we propose an optimization algorithm which we call norm-adapted gradient descent. This algorithm is similar to other gradient-based optimization algorithms like Adam or Adagrad in that it adapts the learning rate of stochastic…

Machine Learning · Computer Science 2020-10-14 David Sprunger

Adaptive first-order optimizers are fundamental tools in deep learning, although they may suffer from poor generalization due to the nonuniform gradient scaling. In this work, we propose AdamL, a novel variant of the Adam optimizer, that…

Machine Learning · Statistics 2023-12-27 Lu Xia , Stefano Massei

This paper proposes a conjugate-gradient-based Adam algorithm blending Adam with nonlinear conjugate gradient methods and shows its convergence analysis. Numerical experiments on text classification and image classification show that the…

Optimization and Control · Mathematics 2020-03-04 Yu Kobayashi , Hideaki Iiduka

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

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…

Machine Learning · Statistics 2025-03-11 Qi Zhang , Yi Zhou , Shaofeng Zou

We introduce MADGRAD, a novel optimization method in the family of AdaGrad adaptive gradient methods. MADGRAD shows excellent performance on deep learning optimization problems from multiple fields, including classification and…

Machine Learning · Computer Science 2021-08-27 Aaron Defazio , Samy Jelassi

Adaptive gradient methods such as Adam have gained extreme popularity due to their success in training complex neural networks and less sensitivity to hyperparameter tuning compared to SGD. However, it has been recently shown that Adam can…

Machine Learning · Computer Science 2019-12-11 Pedro Savarese

The Adam optimizer, often used in Machine Learning for neural network training, corresponds to an underlying ordinary differential equation (ODE) in the limit of very small learning rates. This work shows that the classical Adam algorithm…

Computational Engineering, Finance, and Science · Computer Science 2024-09-17 Abhinab Bhattacharjee , Andrey A. Popov , Arash Sarshar , Adrian Sandu

Adam has become one of the most popular optimizers for training modern deep neural networks, such as transformers. However, its applicability is largely restricted to single-level optimization problems. In this paper, we aim to extend…

Machine Learning · Computer Science 2025-03-07 Xiaochuan Gong , Jie Hao , Mingrui Liu

A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…

Optimization and Control · Mathematics 2026-03-11 Serge Gratton , Philippe L. Toint

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

The Adam optimizer is currently presumably the most popular optimization method in deep learning. In this article we develop an ODE based method to study the Adam optimizer in a fast-slow scaling regime. For fixed momentum parameters and…

Optimization and Control · Mathematics 2025-11-07 Steffen Dereich , Arnulf Jentzen , Sebastian Kassing

We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both…

Machine Learning · Computer Science 2021-02-17 Alina Ene , Huy L. Nguyen , Adrian Vladu

Adaptive gradient algorithms perform gradient-based updates using the history of gradients and are ubiquitous in training deep neural networks. While adaptive gradient methods theory is well understood for minimization problems, the…

Optimization and Control · Mathematics 2020-12-29 Mingrui Liu , Youssef Mroueh , Jerret Ross , Wei Zhang , Xiaodong Cui , Payel Das , Tianbao Yang

Optimization is essential in deep learning. The foundational method upon which most optimizers are built is momentum-based stochastic gradient descent. However, it suffers from two key drawbacks. First, it has noisy and varying gradients,…

Machine Learning · Computer Science 2026-05-22 Saurabh Saini , Kapil Ahuja , Thomas Wick , Saurav Kumar

We propose a new, more general approach to the design of stochastic gradient-based optimization methods for machine learning. In this new framework, optimizers assume access to a batch of gradient estimates per iteration, rather than a…

Machine Learning · Computer Science 2021-12-02 Julius Kunze , James Townsend , David Barber

Adam is one of the most influential adaptive stochastic algorithms for training deep neural networks, which has been pointed out to be divergent even in the simple convex setting via a few simple counterexamples. Many attempts, such as…

Machine Learning · Computer Science 2022-08-09 Congliang Chen , Li Shen , Fangyu Zou , Wei Liu

Adam is a commonly used stochastic optimization algorithm in machine learning. However, its convergence is still not fully understood, especially in the non-convex setting. This paper focuses on exploring hyperparameter settings for the…

Optimization and Control · Mathematics 2025-02-12 Meixuan He , Yuqing Liang , Jinlan Liu , Dongpo Xu

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…

Optimization and Control · Mathematics 2026-02-06 Marianna De Santis , Gabriele Eichfelder , Margherita Porcelli