Related papers: Adam: A Method for Stochastic Optimization
Current state-of-the-art optimizers are adaptive gradient-based optimization methods such as Adam. Recently, there has been an increasing interest in formulating gradient-based optimizers in a probabilistic framework for better modeling the…
These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…
Much of the existing theory on first-order non-smooth optimization is built on a restrictive assumption that the gradients of the objective function are uniformly bounded. We introduce a much more realistic class of generalized Lipschitz…
Deep learning methods - usually consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays omnipresent in data-driven learning problems as well as in scientific…
This paper deals with a network of computing agents aiming to solve an online optimization problem in a distributed fashion, i.e., by means of local computation and communication, without any central coordinator. We propose the gradient…
Stochastic optimizers are central to deep learning, yet widely used methods such as Adam and Adan can degrade in non-stationary or noisy environments, partly due to their reliance on momentum-based magnitude estimates. We introduce Ano, a…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…
When the nonconvex problem is complicated by stochasticity, the sample complexity of stochastic first-order methods may depend linearly on the problem dimension, which is undesirable for large-scale problems. In this work, we propose…
Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…
Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…
Adaptive optimization algorithms, such as Adam and RMSprop, have shown better optimization performance than stochastic gradient descent (SGD) in some scenarios. However, recent studies show that they often lead to worse generalization…
Hyperparameter tuning, particularly the selection of an appropriate learning rate in adaptive gradient training methods, remains a challenge. To tackle this challenge, in this paper, we propose a novel parameter-free optimizer,…
A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…
Adaptive gradient algorithm (AdaGrad) and its variants, such as RMSProp, Adam, AMSGrad, etc, have been widely used in deep learning. Although these algorithms are faster in the early phase of training, their generalization performance is…
An inexact accelerated stochastic Alternating Direction Method of Multipliers (AS-ADMM) scheme is developed for solving structured separable convex optimization problems with linear constraints. The objective function is the sum of a…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
In this work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
We propose a new variant of AMSGrad, a popular adaptive gradient based optimization algorithm widely used for training deep neural networks. Our algorithm adds prior knowledge about the sequence of consecutive mini-batch gradients and…