相关论文: A novel interpretation of Nesterov's acceleration …

Incorporating second order curvature information in gradient based methods have shown to improve convergence drastically despite its computational intensity. In this paper, we propose a stochastic (online) quasi-Newton method with…

In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…

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…

We develop an adaptive Nesterov accelerated proximal gradient (adaNAPG) algorithm for stochastic composite optimization problems, boosting the Nesterov accelerated proximal gradient (NAPG) algorithm through the integration of an adaptive…

This paper generalizes the optimized gradient method (OGM) that achieves the optimal worst-case cost function bound of first-order methods for smooth convex minimization. Specifically, this paper studies a generalized formulation of OGM and…

Current state-of-the-art analyses on the convergence of gradient descent for training neural networks focus on characterizing properties of the loss landscape, such as the Polyak-Lojaciewicz (PL) condition and the restricted strong…

We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from…

When equipped with efficient optimization algorithms, the over-parameterized neural networks have demonstrated high level of performance even though the loss function is non-convex and non-smooth. While many works have been focusing on…

Stochastic optimization is a cornerstone of modern machine learning. This paper studies the generalization performance of two classical stochastic optimization algorithms: stochastic gradient descent (SGD) and Nesterov's accelerated…

We propose Nesterov acceleration with Operator Decomposition (NOD), which extends Nesterov's accelerated gradient descent (NAG) from smooth strongly convex optimization to the broader setting of strongly monotone, Lipschitz operators. The…

We present Nesterov-type acceleration techniques for Alternating Least Squares (ALS) methods applied to canonical tensor decomposition. While Nesterov acceleration turns gradient descent into an optimal first-order method for convex…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

The extrapolation strategy raised by Nesterov, which can accelerate the convergence rate of gradient descent methods by orders of magnitude when dealing with smooth convex objective, has led to tremendous success in training machine…

Motivated by big data applications, first-order methods have been extremely popular in recent years. However, naive gradient methods generally converge slowly. Hence, much efforts have been made to accelerate various first-order methods.…

This paper studies the online convex optimization problem by using an Online Continuous-Time Nesterov Accelerated Gradient method (OCT-NAG). We show that the continuous-time dynamics generated by the online version of the Bregman Lagrangian…

In this technical note, we are concerned with the problem of solving variational inequalities with improved convergence rates. Motivated by Nesterov's accelerated gradient method for convex optimization, we propose a Nesterov's accelerated…

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 application of linear…

In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient…