Related papers: High-probability Convergence Bounds for Nonlinear …
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $\tau$ rounds ago. First, we show that without stochastic…
In this paper, we study the convergence properties of the Stochastic Gradient Descent (SGD) method for finding a stationary point of a given objective function $J(\cdot)$. The objective function is not required to be convex. Rather, our…
Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…
Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…
This paper considers the nonconvex nonsmooth problem in which the objective function is Lipschitz continuous. We focus on the stochastic setting where the algorithm can access stochastic function value evaluations with heavy-tailed noise,…
In the vanishing learning rate regime, stochastic gradient descent (SGD) is now relatively well understood. In this work, we propose to study the basic properties of SGD and its variants in the non-vanishing learning rate regime. The focus…
We study the stochastic linear bandits with heavy-tailed noise. Two principled strategies for handling heavy-tailed noise, truncation and median-of-means, have been introduced to heavy-tailed bandits. Nonetheless, these methods rely on…
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…
We consider the robust linear regression problem in the online setting where we have access to the data in a streaming manner, one data point after the other. More specifically, for a true parameter $\theta^*$, we consider the corrupted…
In this paper, we study the convergence of the Adaptive Moment Estimation (Adam) algorithm under unconstrained non-convex smooth stochastic optimizations. Despite the widespread usage in machine learning areas, its theoretical properties…
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss…
The convergence of stochastic gradient descent is highly dependent on the step-size, especially on non-convex problems such as neural network training. Step decay step-size schedules (constant and then cut) are widely used in practice…
Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…
Dual averaging and gradient descent with their stochastic variants stand as the two canonical recipe books for first-order optimization: Every modern variant can be viewed as a descendant of one or the other. In the convex regime, these…
Stochastic gradient descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood,…
Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to…
We present an algorithm for distributed estimation of an unknown vector parameter $\boldsymbol{\theta}^\ast \in {\mathbb R}^M$ in the presence of heavy-tailed observation and communication noises. Heavy-tailed noises frequently appear,…
Federated learning enables a large amount of edge computing devices to jointly learn a model without data sharing. As a leading algorithm in this setting, Federated Averaging (\texttt{FedAvg}) runs Stochastic Gradient Descent (SGD) in…
We consider the stochastic gradient method with random reshuffling ($\mathsf{RR}$) for tackling smooth nonconvex optimization problems. $\mathsf{RR}$ finds broad applications in practice, notably in training neural networks. In this work,…