English
Related papers

Related papers: Extragradient method with variance reduction for s…

200 papers

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the…

Optimization and Control · Mathematics 2026-04-10 Huaiyi Mu , Yujie Tang , Jie Song , Zhongkui Li

We develop a novel optimistic gradient-type algorithmic framework, combining both Nesterov's acceleration and variance-reduction techniques, to solve a class of generalized equations involving possibly nonmonotone operators in data-driven…

Optimization and Control · Mathematics 2025-08-26 Quoc Tran-Dinh , Nghia Nguyen-Trung

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and…

Optimization and Control · Mathematics 2020-12-22 Shisheng Cui , Uday V. Shanbhag

An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…

Optimization and Control · Mathematics 2019-12-05 Xiaokai Chang , Sanyang Liu , Jianchao Bai , Jun Yang

In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…

Optimization and Control · Mathematics 2020-01-15 Xiaopeng Luo , Xin Xu

The paper concerns with novel first-order methods for monotone variational inequalities. They use a very simple linesearch procedure that takes into account a local information of the operator. Also the methods do not require…

Optimization and Control · Mathematics 2018-03-26 Yura Malitsky

Owing to their stability and convergence speed, extragradient methods have become a staple for solving large-scale saddle-point problems in machine learning. The basic premise of these algorithms is the use of an extrapolation step before…

Optimization and Control · Mathematics 2020-11-06 Yu-Guan Hsieh , Franck Iutzeler , Jérôme Malick , Panayotis Mertikopoulos

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

Optimization and Control · Mathematics 2018-01-15 Shuoguang Yang , Mengdi Wang , Ethan X. Fang

The Stochastic Extragradient (SEG) method is one of the most popular algorithms for solving min-max optimization and variational inequalities problems (VIP) appearing in various machine learning tasks. However, several important questions…

Optimization and Control · Mathematics 2022-02-23 Eduard Gorbunov , Hugo Berard , Gauthier Gidel , Nicolas Loizou

Stochastic second-order methods achieve fast local convergence in strongly convex optimization by using noisy Hessian estimates to precondition the gradient. However, these methods typically reach superlinear convergence only when the…

Optimization and Control · Mathematics 2024-11-12 Ruichen Jiang , Michał Dereziński , Aryan Mokhtari

In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems, for which we have access to exact information of constraints and noisy function values of the objective. We propose a Bregman linearized augmented…

Optimization and Control · Mathematics 2025-04-15 Qiankun Shi , Xiao Wang , Hao Wang

In this paper, we present a novel stochastic method for solving variational inequalities (VI) in the context of Markovian noise. By leveraging Extragradient technique, we can productively solve VI optimization problems characterized by…

Optimization and Control · Mathematics 2026-05-18 Vladimir Solodkin , Michael Ermoshin , Roman Gavrilenko , Aleksandr Beznosikov

Variational inequalities are a universal optimization paradigm that is interesting in itself, but also incorporates classical minimization and saddle point problems. Modern realities encourage to consider stochastic formulations of…

Optimization and Control · Mathematics 2024-03-27 Alexander Pichugin , Maksim Pechin , Aleksandr Beznosikov , Alexander Gasnikov

This work proposes a universal and adaptive second-order method for minimizing second-order smooth, convex functions. Our algorithm achieves $O(\sigma / \sqrt{T})$ convergence when the oracle feedback is stochastic with variance $\sigma^2$,…

Optimization and Control · Mathematics 2022-12-13 Kimon Antonakopoulos , Ali Kavis , Volkan Cevher

In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving…

Optimization and Control · Mathematics 2023-06-21 Georgios Kotsalis , Guanghui Lan , Tianjiao Li

We consider a step search method for continuous optimization under a stochastic setting where the function values and gradients are available only through inexact probabilistic zeroth- and first-order oracles. Unlike the stochastic gradient…

Optimization and Control · Mathematics 2023-11-03 Billy Jin , Katya Scheinberg , Miaolan Xie

Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…

Optimization and Control · Mathematics 2025-02-06 Roman Emelyanov , Andrey Tikhomirov , Aleksandr Beznosikov , Alexander Gasnikov

For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…

Optimization and Control · Mathematics 2022-02-16 Meng Li , Paul Grigas , Alper Atamturk

In this paper we introduce new methods for convex optimization problems with inexact stochastic oracle. First method is an extension of the intermediate gradient method proposed by Devolder, Glineur and Nesterov for problems with inexact…

Optimization and Control · Mathematics 2015-12-08 Pavel Dvurechensky , Alexander Gasnikov