Related papers: Accelerated Gradient Methods for Sparse Statistica…
In a Hilbert setting, we develop a gradient-based dynamic approach for fast solving convex optimization problems. By applying time scaling, averaging, and perturbation techniques to the continuous steepest descent (SD), we obtain…
We modify Nesterov's constant step gradient method for strongly convex functions with Lipschitz continuous gradient described in Nesterov's book. Nesterov shows that $f(x_k) - f^* \leq L \prod_{i=1}^k (1 - \alpha_k) \| x_0 - x^* \|_2^2$…
In this paper, we develop a unified convergence analysis framework for the Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in [20, Tran-Dinh et al, 2015] Unlike[20], the new analysis covers three settings in a single…
Despite the recent growth of theoretical studies and empirical successes of neural networks, gradient backpropagation is still the most widely used algorithm for training such networks. On the one hand, we have deterministic or full…
We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves…
Accelerated algorithms have broad applications in large-scale optimization, due to their generality and fast convergence. However, their stability in the practical setting of noise-corrupted gradient oracles is not well-understood. This…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
In this paper, we propose a new, simplified high probability analysis of AdaGrad for smooth, non-convex problems. More specifically, we focus on a particular accelerated gradient (AGD) template (Lan, 2020), through which we recover the…
The goal of this paper is to reduce the total complexity of gradient-based methods for two classes of problems: affine-constrained composite convex optimization and bilinear saddle-point structured non-smooth convex optimization. Our…
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…
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…
Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…
Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…
In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh to tackle nonsmooth and strongly convex composite problems. We prove that our proposed algorithm, dubbed geometric proximal gradient method…
In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…
We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…
Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence…
Recent studies incorporate Nesterov's accelerated gradient method for the acceleration of gradient based training. The Nesterov's Accelerated Quasi-Newton (NAQ) method has shown to drastically improve the convergence speed compared to the…
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 develop a theoretical foundation for the application of Nesterov's accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the…