Related papers: Non-strongly-convex smooth stochastic approximatio…
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…
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 work, we present a globalized stochastic semismooth Newton method for solving stochastic optimization problems involving smooth nonconvex and nonsmooth convex terms in the objective function. We assume that only noisy gradient and…
Stochastic gradient descent (SGD) on a low-rank factorization is commonly employed to speed up matrix problems including matrix completion, subspace tracking, and SDP relaxation. In this paper, we exhibit a step size scheme for SGD on a…
The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have…
This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…
Stochastic gradient descent is the method of choice for large scale optimization of machine learning objective functions. Yet, its performance is greatly variable and heavily depends on the choice of the stepsizes. This has motivated a…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…
This paper deals with convex nonsmooth optimization problems. We introduce a general smooth approximation framework for the original function and apply random (accelerated) coordinate descent methods for minimizing the corresponding smooth…
This paper proposes a stochastic gradient descent method with an adaptive Gaussian noise term for the global minimization of nearly convex functions, which are nonconvex and possess multiple strict local minimizers. The noise term,…
We present a stochastic descent algorithm for unconstrained optimization that is particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained optimization and…
Online and stochastic gradient methods have emerged as potent tools in large scale optimization with both smooth convex and nonsmooth convex problems from the classes $C^{1,1}(\reals^p)$ and $C^{1,0}(\reals^p)$ respectively. However to our…
Motivated by applications arising from large scale optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving unconstrained convex optimization problems. The convergence analysis of the SQN methods,…
Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In…
We present a novel statistical inference framework for convex empirical risk minimization, using approximate stochastic Newton steps. The proposed algorithm is based on the notion of finite differences and allows the approximation of a…
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…
The purpose of this manuscript is to derive new convergence results for several subgradient methods applied to minimizing nonsmooth convex functions with H\"olderian growth. The growth condition is satisfied in many applications and…
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…
We discuss non-Euclidean deterministic and stochastic algorithms for optimization problems with strongly and uniformly convex objectives. We provide accuracy bounds for the performance of these algorithms and design methods which are…
Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…