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We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to…
Training Artificial Neural Networks (ANNs) with Stochastic Gradient Descent (SGD) frequently encounters difficulties, including substantial computing expense and the risk of converging to local optima, attributable to its dependence on…
Variance reduction (VR) methods employ stochastic gradients with decreasing variance, and they have been widely applied to solve large-scale optimization problems in machine learning because of their efficiency. Existing theoretical studies…
Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…
Stochastic momentum methods have been widely adopted in training deep neural networks. However, their theoretical analysis of convergence of the training objective and the generalization error for prediction is still under-explored. This…
Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…
Recently, flat-minima optimizers, which seek to find parameters in low-loss neighborhoods, have been shown to improve a neural network's generalization performance over stochastic and adaptive gradient-based optimizers. Two methods have…
Many recent successes of machine learning went hand in hand with advances in optimization. The exchange of ideas between these fields has worked both ways, with machine learning building on standard optimization procedures such as gradient…
We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately…
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…
Understanding the algorithmic bias of \emph{stochastic gradient descent} (SGD) is one of the key challenges in modern machine learning and deep learning theory. Most of the existing works, however, focus on \emph{very small or even…
Stochastic gradient descent (SGD) now acts as a fundamental part of optimization in current machine learning. Meanwhile, deep learning architectures have shown outstanding performance in a wide range of fields, such as natural language…
In federated distributed learning, the goal is to optimize a global training objective defined over distributed devices, where the data shard at each device is sampled from a possibly different distribution (a.k.a., heterogeneous or non…
In this paper, we propose a novel kernel stochastic gradient descent (SGD) algorithm for large-scale supervised learning with general losses. Compared to traditional kernel SGD, our algorithm improves efficiency and scalability through an…
We give a new separation result between the generalization performance of stochastic gradient descent (SGD) and of full-batch gradient descent (GD) in the fundamental stochastic convex optimization model. While for SGD it is well-known that…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some…
Gradient descent (GD) and stochastic gradient descent (SGD) are the workhorses of large-scale machine learning. While classical theory focused on analyzing the performance of these methods in convex optimization problems, the most notable…
Optimization theory serves as a pivotal scientific instrument for achieving optimal system performance, with its origins in economic applications to identify the best investment strategies for maximizing benefits. Over the centuries, from…
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…