Adam) and accelerated schemes (e.g.

We thank all reviewers for comments. We are glad to see our work commented as "promising"(R3), "effective"(R6), We address their concerns below. Writing We'll rephrase remarks, e.g."Examples give hints to local behavior of optimizers in deep learning". Q2.a Assumptions We list assumptions (1)-(3) as below: Numerically, we need a small β (e.g 0.3) or large t . We also tried default β with large t, results similar to Fig.3(d).

This paper proposes an efficient optimizer called AdaPlus which integrates Nesterov momentum and precise stepsize adjustment on AdamW basis. AdaPlus combines the advantages of AdamW, Nadam, and AdaBelief and, in particular, does not introduce any extra hyper-parameters. We perform extensive experimental evaluations on three machine learning tasks to validate the effectiveness of AdaPlus. The experiment results validate that AdaPlus (i) among all the evaluated adaptive methods, performs most comparable with (even slightly better than) SGD with momentum on image classification tasks and (ii) outperforms other state-of-the-art optimizers on language modeling tasks and illustrates pretty high stability when training GANs. The experiment code of AdaPlus will be accessible at: https://github.com/guanleics/AdaPlus.

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 takes into account the loss function information to attain better generalization results. We provide sufficient conditions that together with the Polyak-Lojasiewicz inequality, ensure the linear convergence of AdamL. As a byproduct of our analysis, we prove similar convergence properties for the EAdam, and AdaBelief optimizers. Experimental results on benchmark functions show that AdamL typically achieves either the fastest convergence or the lowest objective function values when compared to Adam, EAdam, and AdaBelief. These superior performances are confirmed when considering deep learning tasks such as training convolutional neural networks, training generative adversarial networks using vanilla convolutional neural networks, and long short-term memory networks. Finally, in the case of vanilla convolutional neural networks, AdamL stands out from the other Adam's variants and does not require the manual adjustment of the learning rate during the later stage of the training.

Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each gradient direction. In this paper, we propose a novel approach to designing the preconditioning matrix by utilizing the gradient difference between two successive steps as the diagonal elements. These diagonal elements are closely related to the Hessian and can be perceived as an approximation of the inner product between the Hessian row vectors and difference of the adjacent parameter vectors. Additionally, we introduce an auto-switching function that enables the preconditioning matrix to switch dynamically between Stochastic Gradient Descent (SGD) and the adaptive optimizer. Based on these two techniques, we develop a new optimizer named AGD that enhances the generalization performance. We evaluate AGD on public datasets of Natural Language Processing (NLP), Computer Vision (CV), and Recommendation Systems (RecSys). Our experimental results demonstrate that AGD outperforms the state-of-the-art (SOTA) optimizers, achieving highly competitive or significantly better predictive performance. Furthermore, we analyze how AGD is able to switch automatically between SGD and the adaptive optimizer and its actual effects on various scenarios.