相关论文: Restarted Nonconvex Accelerated Gradient Descent: …

There is a growing interest in using robust control theory to analyze and design optimization and machine learning algorithms. This paper studies a class of nonconvex optimization problems whose cost functions satisfy the so-called…

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…

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…

We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational…

Low-rank and nonsmooth matrix optimization problems capture many fundamental tasks in statistics and machine learning. While significant progress has been made in recent years in developing efficient methods for \textit{smooth} low-rank…

We study the trade-offs between convergence rate and robustness to gradient errors in designing a first-order algorithm. We focus on gradient descent (GD) and accelerated gradient (AG) methods for minimizing strongly convex functions when…

Due to its simplicity and efficiency, the first-order gradient method has been extensively employed in training neural networks. Although the optimization problem of the neural network is non-convex, recent research has proved that the…

We consider the problem of minimizing a strongly convex smooth function where the gradients are subject to additive worst-case deterministic errors that are square-summable. We study the trade-offs between the convergence rate and…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

In this paper we propose several adaptive gradient methods for stochastic optimization. Unlike AdaGrad-type of methods, our algorithms are based on Armijo-type line search and they simultaneously adapt to the unknown Lipschitz constant of…

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise…

We study the convergence rate of first-order methods for rectangular matrix factorization, which is a canonical nonconvex optimization problem. Specifically, given a rank-$r$ matrix $\mathbf{A}\in\mathbb{R}^{m\times n}$, we prove that…

There is widespread sentiment that it is not possible to effectively utilize fast gradient methods (e.g. Nesterov's acceleration, conjugate gradient, heavy ball) for the purposes of stochastic optimization due to their instability and error…

Riemannian accelerated gradient methods have been well studied for smooth optimization, typically treating geodesically convex and geodesically strongly convex cases separately. However, their extension to nonsmooth problems on manifolds…

We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both…

We propose a fast second-order method that can be used as a drop-in replacement for current deep learning solvers. Compared to stochastic gradient descent (SGD), it only requires two additional forward-mode automatic differentiation…

We propose a new \textit{randomized Bregman (block) coordinate descent} (RBCD) method for minimizing a composite problem, where the objective function could be either convex or nonconvex, and the smooth part are freed from the global…

Accelerated algorithms for minimizing smooth strongly convex functions usually require knowledge of the strong convexity parameter $\mu$. In the case of an unknown $\mu$, current adaptive techniques are based on restart schemes. When the…

We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of…