Related papers: Convergence rates for the Adam optimizer
Optimizer is an essential component for the success of deep learning, which guides the neural network to update the parameters according to the loss on the training set. SGD and Adam are two classical and effective optimizers on which…
Distributed data mining is an emerging research topic to effectively and efficiently address hard data mining tasks using big data, which are partitioned and computed on different worker nodes, instead of one centralized server.…
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…
Gradient descent algorithm is the most utilized method when optimizing machine learning issues. However, there exists many local minimums and saddle points in the loss function, especially for high dimensional non-convex optimization…
Within the current sphere of deep learning research, despite the extensive application of optimization algorithms such as Stochastic Gradient Descent (SGD) and Adaptive Moment Estimation (Adam), there remains a pronounced inadequacy in…
Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning.…
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…
In many numerical simulations stochastic gradient descent (SGD) type optimization methods perform very effectively in the training of deep neural networks (DNNs) but till this day it remains an open problem of research to provide a…
Neural networks are usually trained by some form of stochastic gradient descent (SGD)). A number of strategies are in common use intended to improve SGD optimization, such as learning rate schedules, momentum, and batching. These are…
Stochastic gradient descent (SGD) is a workhorse algorithm for solving large-scale optimization problems in data science and machine learning. Understanding the convergence of SGD is hence of fundamental importance. In this work we examine…
Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights…
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…
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…
Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are the choice of algorithms for solving non-convex problems (especially deep learning), there still remain big gaps between the…
Deep learning optimization relies heavily on the assumption of smooth loss landscapes, a condition systematically violated by modern architectures due to non-smooth components such as ReLU activations and quantization operators. In such…
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…
Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…
We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…
Adaptive gradient methods such as RMSProp and Adam use exponential moving estimate of the squared gradient to compute adaptive step sizes, achieving better convergence than SGD in face of noisy objectives. However, Adam can have undesirable…
Averaging scheme has attracted extensive attention in deep learning as well as traditional machine learning. It achieves theoretically optimal convergence and also improves the empirical model performance. However, there is still a lack of…