相关论文: Accelerated Over-Relaxation Heavy-Ball Method: Ach…

In this paper, we study a stochastic strongly convex optimization problem and propose three classes of variable sample-size stochastic first-order methods including the standard stochastic gradient descent method, its accelerated variant,…

We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…

The stochastic heavy ball momentum (SHBM) method has gained considerable popularity as a scalable approach for solving large-scale optimization problems. However, one limitation of this method is its reliance on prior knowledge of certain…

Adaptive momentum methods have recently attracted a lot of attention for training of deep neural networks. They use an exponential moving average of past gradients of the objective function to update both search directions and learning…

We consider convex optimization problems with the objective function having Lipshitz-continuous $p$-th order derivative, where $p\geq 1$. We propose a new tensor method, which closes the gap between the lower…

This paper provides a rigorous convergence rate and complexity analysis for a recently introduced framework, called PDE acceleration, for solving problems in the calculus of variations, and explores applications to obstacle problems. PDE…

We propose a hybrid control algorithm that guarantees fast convergence and uniform global asymptotic stability of the unique minimizer of a continuously differentiable, convex objective function. The algorithm, developed using hybrid system…

This paper investigates accelerating the convergence of distributed optimization algorithms on non-convex problems. We propose a distributed primal-dual stochastic gradient descent~(SGD) equipped with "powerball" method to accelerate. We…

We present an accelerated relax-and-round algorithm for concave coverage problems, which generalize the classic maximum coverage problem. Building on the relax-and-round framework of Barman et al. [STACS 2021], we propose two significant…

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 consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…

We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…

Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The…

We analyze gradient descent with Polyak heavy-ball momentum (HB) whose fixed momentum parameter $\beta \in (0, 1)$ provides exponential decay of memory. Building on Kovachki and Stuart (2021), we prove that on an exponentially attractive…

The Bregman-Kaczmarz method is an iterative method which can solve strongly convex problems with linear constraints and uses only one or a selected number of rows of the system matrix in each iteration, thereby making it amenable for…

Q-learning is a widely used algorithm in reinforcement learning (RL), but its convergence can be slow, especially when the discount factor is close to one. Successive Over-Relaxation (SOR) Q-learning, which introduces a relaxation factor to…

In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…

We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…

The extensive-form game has been studied considerably in recent years. It can represent games with multiple decision points and incomplete information, and hence it is helpful in formulating games with uncertain inputs, such as poker. We…

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike…