Related papers: Stochastic Gradient Descent with Momentum is Algor…
Non-convex optimization problems are ubiquitous in machine learning, especially in Deep Learning. While such complex problems can often be successfully optimized in practice by using stochastic gradient descent (SGD), theoretical analysis…
This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
For overparameterized optimization tasks, such as those found in modern machine learning, global minima are generally not unique. In order to understand generalization in these settings, it is vital to study to which minimum an optimization…
Momentum has become a crucial component in deep learning optimizers, necessitating a comprehensive understanding of when and why it accelerates stochastic gradient descent (SGD). To address the question of ''when'', we establish a…
Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…
The performance of fully synchronized distributed systems has faced a bottleneck due to the big data trend, under which asynchronous distributed systems are becoming a major popularity due to their powerful scalability. In this paper, we…
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on…
Momentum method has been used extensively in optimizers for deep learning. Recent studies show that distributed training through K-step averaging has many nice properties. We propose a momentum method for such model averaging approaches. At…
We study the generalization properties of the popular stochastic optimization method known as stochastic gradient descent (SGD) for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the…
This work studies the generalization error of gradient methods. More specifically, we focus on how training steps $T$ and step-size $\eta$ might affect generalization in smooth stochastic convex optimization (SCO) problems. We first provide…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…
We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…
Stochastic Gradient Descent (SGD) based methods have been widely used for training large-scale machine learning models that also generalize well in practice. Several explanations have been offered for this generalization performance, a…
We develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive application of linear…
We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…
Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…
The growing size of available data has attracted increasing interest in solving minimax problems in a decentralized manner for various machine learning tasks. Previous theoretical research has primarily focused on the convergence rate and…