相关论文: ANITA: An Optimal Loopless Accelerated Variance-Re…

We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…

Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps periodically, gradient descent's textbook $LD^2/2T$ convergence guarantees can be improved by constant factors, conjecturing an accelerated rate strictly…

We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for…

We study the monotone inclusion problem $0\in F(z)+A(z)$, where $F$ is monotone and Lipschitz, and $A$ is maximally monotone, a framework that encompasses monotone variational inequalities and convex-concave saddle-point problems with…

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing composite nonconvex finite-sum functions. It integrates three acceleration techniques: adaptive…

This paper describes a novel algorithmic framework to minimize a finite-sum of functions available over a network of nodes. The proposed framework, that we call~\GTVR, is stochastic and decentralized, and thus is particularly suitable for…

This paper proposes a set of new error criteria and learning approaches, Adaptive Normalized Risk-Averting Training (ANRAT), to attack the non-convex optimization problem in training deep neural networks (DNNs). Theoretically, we…

We develop and analyze a variant of the SARAH algorithm, which does not require computation of the exact gradient. Thus this new method can be applied to general expectation minimization problems rather than only finite sum problems. While…

In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable…

In this paper, we develop two new randomized block-coordinate optimistic gradient algorithms to approximate a solution of nonlinear equations in large-scale settings, which are called root-finding problems. Our first algorithm is…

Recent advances in randomized incremental methods for minimizing $L$-smooth $\mu$-strongly convex finite sums have culminated in tight complexity of $\tilde{O}((n+\sqrt{n L/\mu})\log(1/\epsilon))$ and $O(n+\sqrt{nL/\epsilon})$, where…

In this paper, we consider constrained optimization problems with convex, smooth objective and constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class…

In this paper, we provide the universal first-order methods of Composite Optimization with new complexity analysis. It delivers some universal convergence guarantees, which are not linked directly to any parametric problem class. However,…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…

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…

In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…