Related papers: Accelerated Stochastic Gradient Descent for Minimi…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…
For solving pseudo-convex global optimization problems, we present a novel fully adaptive steepest descent method (or ASDM) without any hard-to-estimate parameters. For the step-size regulation in an $\varepsilon$-normalized direction, we…
Gradient descent is an important class of iterative algorithms for minimizing convex functions. Classically, gradient descent has been a sequential and synchronous process. Distributed and asynchronous variants of gradient descent have been…
The article discusses distributed gradient-descent algorithms for computing local and global minima in nonconvex optimization. For local optimization, we focus on distributed stochastic gradient descent (D-SGD)--a simple network-based…
We study the convergence rate of the proximal incremental aggregated gradient (PIAG) method for minimizing the sum of a large number of smooth component functions (where the sum is strongly convex) and a non-smooth convex function. At each…
Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…
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…
In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…
In this paper, we propose a simple variant of the original stochastic variance reduction gradient (SVRG), where hereafter we refer to as the variance reduced stochastic gradient descent (VR-SGD). Different from the choices of the snapshot…
Minimax optimization problems have attracted significant attention in recent years due to their widespread application in numerous machine learning models. To solve the minimax problem, a wide variety of stochastic optimization methods have…
Stochastic gradient method (SGM) has been popularly applied to solve optimization problems with objective that is stochastic or an average of many functions. Most existing works on SGMs assume that the underlying problem is unconstrained or…
This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…
We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…
In this paper, we present CT-AGD (Curvature-Tuned Accelerated Gradient Descent), an optimization method for non-convex optimization problems in deep learning training tasks. CT-AGD is a general boosting procedure that accelerates…
In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…
Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the…
Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate…