相关论文: Variance-based stochastic extragradient methods wi…

Variance-reduced stochastic gradient methods have gained popularity in recent times. Several variants exist with different strategies for the storing and sampling of gradients and this work concerns the interactions between these two…

We provide a general framework for the stability of solutions to stochastic partial differential equations with respect to perturbations of the drift. More precisely, we consider stochastic partial differential equations with drift given as…

We develop a novel and single-loop variance-reduced algorithm to solve a class of stochastic nonconvex-convex minimax problems involving a nonconvex-linear objective function, which has various applications in different fields such as…

In this paper, we introduce a new approach to proving the convergence of the Stochastic Approximation (SA) and the Stochastic Gradient Descent (SGD) algorithms. The new approach is based on a concept called GSLLN (Generalized Strong Law of…

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…

In this paper, we study federated optimization for solving stochastic variational inequalities (VIs), a problem that has attracted growing attention in recent years. Despite substantial progress, a significant gap remains between existing…

This work is concerned with robust filtering of nonlinear sampled-data systems with and without exact discrete-time models. A linear matrix inequality (LMI) based approach is proposed for the design of robust $H_{\infty}$ observers for a…

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…

Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a…

Adaptive gradient methods, such as AdaGrad, are among the most successful optimization algorithms for neural network training. While these methods are known to achieve better dimensional dependence than stochastic gradient descent (SGD) for…

This work presents the convergence rate analysis of stochastic variants of the broad class of direct-search methods of directional type. It introduces an algorithm designed to optimize differentiable objective functions $f$ whose values can…

We study distributed optimization algorithms for minimizing the average of \emph{heterogeneous} functions distributed across several machines with a focus on communication efficiency. In such settings, naively using the classical stochastic…

Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…

Stochastic particle-optimization sampling (SPOS) is a recently-developed scalable Bayesian sampling framework that unifies stochastic gradient MCMC (SG-MCMC) and Stein variational gradient descent (SVGD) algorithms based on Wasserstein…

We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse and efficient sub-structure. Our regularizer is only assumed to be lower semi-continuous and prox-bounded. We combine an adaptive…

In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in…

We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…

We exploit the observation that stochastic variational inference (SVI) is a form of annealing and present a modified SVI approach -- applicable to both large and small datasets -- that allows the amount of annealing done by SVI to be tuned.…

Stochastic gradient methods are dominant in nonconvex optimization especially for deep models but have low asymptotical convergence due to the fixed smoothness. To address this problem, we propose a simple yet effective method for improving…

We propose a novel stochastic smoothing accelerated gradient (SSAG) method for general constrained nonsmooth convex composite optimization, and analyze the convergence rates. The SSAG method allows various smoothing techniques, and can deal…