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We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $\beta_{1}$ (typically between $0.9$ and $0.99$). In…

Since its invention in 2014, the Adam optimizer has received tremendous attention. On one hand, it has been widely used in deep learning and many variants have been proposed, while on the other hand their theoretical convergence property…

Value-based deep Reinforcement Learning (RL) algorithms suffer from the estimation bias primarily caused by function approximation and temporal difference (TD) learning. This problem induces faulty state-action value estimates and therefore…

A crucial component of machine learning algorithms is minimizing loss functions with less computational cost and less oscillations. While adaptive learning rate-based optimizers have been widely used for real-world tasks, they do not…

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…

Momentum based optimizers are central to a wide range of machine learning applications. These typically rely on an Exponential Moving Average (EMA) of gradients, which decays exponentially the present contribution of older gradients. This…

Adam-type optimizers, as a class of adaptive moment estimation methods with the exponential moving average scheme, have been successfully used in many applications of deep learning. Such methods are appealing due to the capability on…

In the context of stochastic gradient descent(SGD) and adaptive moment estimation (Adam),researchers have recently proposed optimization techniques that transition from Adam to SGD with the goal of improving both convergence and…

Artificial intelligence systems, especially those using machine learning, are being deployed in domains from hiring to loan issuance in order to automate these complex decisions. Judging both the effectiveness and fairness of these AI…

Machine learning and data mining algorithms have been increasingly used recently to support decision-making systems in many areas of high societal importance such as healthcare, education, or security. While being very efficient in their…

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., $\beta_2$, in a problem-dependent manner. There have been many…

It is widely believed that stochastic gradient descent (SGD) performs significantly worse than adaptive optimizers such as Adam in pre-training Large Language Models (LLMs). Yet the underlying reason for this gap remains unclear. In this…

Data-driven decision making is gaining prominence with the popularity of various machine learning models. Unfortunately, real-life data used in machine learning training may capture human biases, and as a result the learned models may lead…

In the context of the optimization of Deep Neural Networks, we propose to rescale the learning rate using a new technique of automatic differentiation. This technique relies on the computation of the {\em curvature}, a second order…

Currently, widely used first-order deep learning optimizers include non-adaptive learning rate optimizers and adaptive learning rate optimizers. The former is represented by SGDM (Stochastic Gradient Descent with Momentum), while the latter…

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,…

Gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We find that the discrete steps of gradient descent implicitly regularize models by penalizing gradient…

Adam outperforms SGD when training language models. Yet this advantage is not well-understood theoretically -- previous convergence analysis for Adam and SGD mainly focuses on the number of steps $T$ and is already minimax-optimal in…

Stochastic Gradient Descent (SGD) with adaptive steps is widely used to train deep neural networks and generative models. Most theoretical results assume that it is possible to obtain unbiased gradient estimators, which is not the case in…