Related papers: Data-Driven Minimax Optimization with Expectation …

Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the…

This paper considers the problem of minimizing a convex expectation function with a set of inequality convex expectation constraints. We present a computable stochastic approximation type algorithm, namely the stochastic linearized proximal…

We focus on solving constrained convex optimization problems using mini-batch stochastic gradient descent. Dynamic sample size rules are presented which ensure a descent direction with high probability. Empirical results from two…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

Stochastic gradient methods (SGMs) have been widely used for solving stochastic optimization problems. A majority of existing works assume no constraints or easy-to-project constraints. In this paper, we consider convex stochastic…

This paper develops a distributed primal-dual algorithm via event-triggered mechanism to solve a class of convex optimization problems subject to local set constraints, coupled equality and inequality constraints. Different from some…

We develop a novel unified randomized block-coordinate primal-dual algorithm to solve a class of nonsmooth constrained convex optimization problems, which covers different existing variants and model settings from the literature. We prove…

A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…

In this paper, we focus on the problem of stochastic optimization where the objective function can be written as an expectation function over a closed convex set. We also consider multiple expectation constraints which restrict the domain…

The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly…

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However,…

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…

We consider a wide range of regularized stochastic minimization problems with two regularization terms, one of which is composed with a linear function. This optimization model abstracts a number of important applications in artificial…

This paper develops projection-free algorithms for online convex optimization with stochastic constraints. We design an online primal-dual projection-free framework that can take any projection-free algorithms developed for online convex…

We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…

In recent years, nonconvex minimax problems have attracted significant attention due to their broad applications in machine learning, including generative adversarial networks, robust optimization and adversarial training. Most existing…

Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main…

This paper considers stochastic-constrained stochastic optimization where the stochastic constraint is to satisfy that the expectation of a random function is below a certain threshold. In particular, we study the setting where data samples…