Related papers: Finite-Time Analysis of Stochastic Gradient Descen…

The stochastic mirror descent (SMD) algorithm is a general class of training algorithms, which includes the celebrated stochastic gradient descent (SGD), as a special case. It utilizes a mirror potential to influence the implicit bias of…

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Differentially private stochastic gradient descent (DP-SGD) has become the standard algorithm for training machine learning models with rigorous privacy guarantees. Despite its widespread use, the theoretical understanding of its long-run…

This paper is concerned with minimizing the average of $n$ cost functions over a network in which agents may communicate and exchange information with each other. We consider the setting where only noisy gradient information is available.…

In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of…

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

We study the mixing properties for stochastic accelerated gradient descent (SAGD) on least-squares regression. First, we show that stochastic gradient descent (SGD) and SAGD are simulating the same invariant distribution. Motivated by this,…

The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We…

In this work, we investigate the dynamics of stochastic gradient descent (SGD) when training a single-neuron autoencoder with linear or ReLU activation on orthogonal data. We show that for this non-convex problem, randomly initialized SGD…

A theoretical, and potentially also practical, problem with stochastic gradient descent is that trajectories may escape to infinity. In this note, we investigate uniform boundedness properties of iterates and function values along the…

Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective function $f$ that is locally strongly convex with a sub--quadratic tail. This setting covers…

Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit…

We aim to provide a unified convergence analysis for permutation-based Stochastic Gradient Descent (SGD), where data examples are permuted before each epoch. By examining the relations among permutations, we categorize existing…

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 in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Following the same routine as [SSJ20], we continue to present the theoretical analysis for stochastic gradient descent with momentum (SGD with momentum) in this paper. Differently, for SGD with momentum, we demonstrate it is the two…

Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…

Understanding the convergence performance of asynchronous stochastic gradient descent method (Async-SGD) has received increasing attention in recent years due to their foundational role in machine learning. To date, however, most of the…

Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…

It is well-known that the reparameterisation gradient estimator, which exhibits low variance in practice, is biased for non-differentiable models. This may compromise correctness of gradient-based optimisation methods such as stochastic…