Related papers: SGD without Replacement: Sharper Rates for General…

Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…

In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an $(\epsilon, O(\epsilon^{0.5}))$-approximate second-order stationary point in…

With a weighting scheme proportional to t, a traditional stochastic gradient descent (SGD) algorithm achieves a high probability convergence rate of O({\kappa}/T) for strongly convex functions, instead of O({\kappa} ln(T)/T). We also prove…

This article examines the implicit regularization effect of Stochastic Gradient Descent (SGD). We consider the case of SGD without replacement, the variant typically used to optimize large-scale neural networks. We analyze this algorithm in…

Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

We study stochastic gradient descent (SGD) and the stochastic heavy ball method (SHB, otherwise known as the momentum method) for the general stochastic approximation problem. For SGD, in the convex and smooth setting, we provide the first…

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

For solving finite-sum optimization problems, SGD without replacement sampling is empirically shown to outperform SGD. Denoting by $n$ the number of components in the cost and $K$ the number of epochs of the algorithm , several recent works…

This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be…

Motivated by broad applications in reinforcement learning and machine learning, this paper considers the popular stochastic gradient descent (SGD) when the gradients of the underlying objective function are sampled from Markov processes.…

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

We consider the generalization error associated with stochastic gradient descent on a smooth convex function over a compact set. We show the first bound on the generalization error that vanishes when the number of iterations $T$ and the…

Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for example the learning rate) of the algorithm. In this paper we…

When solving finite-sum minimization problems, two common alternatives to stochastic gradient descent (SGD) with theoretical benefits are random reshuffling (SGD-RR) and shuffle-once (SGD-SO), in which functions are sampled in cycles…

The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…

There has been a growing effort in studying the distributed optimization problem over a network. The objective is to optimize a global function formed by a sum of local functions, using only local computation and communication. Literature…

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and…