Related papers: Oblivious Stochastic Composite Optimization
Existing decentralized algorithms usually require knowledge of problem parameters for updating local iterates. For example, the hyperparameters (such as learning rate) usually require the knowledge of Lipschitz constant of the global…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We consider randomized block coordinate stochastic mirror descent (RBSMD) methods for solving high-dimensional stochastic optimization problems with strongly convex objective functions. Our goal is to develop RBSMD schemes that achieve a…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…
In this paper, we address learning problems for high dimensional data. Previously, oblivious random projection based approaches that project high dimensional features onto a random subspace have been used in practice for tackling…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
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…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
In this work, we describe a generic approach to show convergence with high probability for both stochastic convex and non-convex optimization with sub-Gaussian noise. In previous works for convex optimization, either the convergence is only…
An algorithm is said to be adaptive to a certain parameter (of the problem) if it does not need a priori knowledge of such a parameter but performs competitively to those that know it. This dissertation presents our work on adaptive…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
We analyze the global and local behavior of gradient-like flows under stochastic errors towards the aim of solving convex optimization problems with noisy gradient input. We first study the unconstrained differentiable convex case, using a…
In this paper, we investigate the non-asymptotic stationary convergence behavior of Stochastic Mirror Descent (SMD) for nonconvex optimization. We focus on a general class of nonconvex nonsmooth stochastic optimization problems, in which…
We consider decentralized stochastic convex optimization on connected network, in which gradients of agents are unavailable and each agent can query only noisy function values of its own local objective. The goal is to minimize the average…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
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…