Related papers: Mean Gradient Descent: An optimization approach fo…

This paper provides a unified treatment to the recovery of structured signals living in a star-shaped set from general quantized measurements $\mathcal{Q}(\mathbf{A}\mathbf{x}-\mathbf{\tau})$, where $\mathbf{A}$ is a sensing matrix,…

The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…

This paper investigates the problem of recovering hyperspectral (HS) images from single RGB images. To tackle such a severely ill-posed problem, we propose a physically-interpretable, compact, efficient, and end-to-end learning-based…

In the recent years, various gradient descent algorithms including the methods of gradient descent, gradient descent with momentum, adaptive gradient (AdaGrad), root-mean-square propagation (RMSProp) and adaptive moment estimation (Adam)…

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…

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 gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…

Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…

We address the optimization problem of simultaneously minimizing multiple objective functionals over a family of probability distributions. This type of Multi-Objective Distributional Optimization commonly arises in machine learning and…

We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural…

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…

Memory-efficient optimization methods have recently gained increasing attention for scaling full-parameter training of large language models under the GPU-memory bottleneck. Existing approaches either lack clear convergence guarantees, or…

Distributed stochastic gradient descent~(DSGD) has been widely used for optimizing large-scale machine learning models, including both convex and non-convex models. With the rapid growth of model size, huge communication cost has been the…

Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…

Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For…

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined…

In recent literature, a general two step procedure has been formulated for solving the problem of phase retrieval. First, a spectral technique is used to obtain a constant-error initial estimate, following which, the estimate is refined to…

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

It is folklore that reusing training data more than once can improve the statistical efficiency of gradient-based learning. However, beyond linear regression, the theoretical advantage of full-batch gradient descent (GD, which always reuses…