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In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages…

Optimization and Control · Mathematics 2020-05-26 Parvin Nazari , Davoud Ataee Tarzanagh , George Michailidis

We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…

Machine Learning · Computer Science 2020-07-09 Maria-Luiza Vladarean , Ahmet Alacaoglu , Ya-Ping Hsieh , Volkan Cevher

We study monotone variational inequalities that can arise as optimality conditions for constrained convex optimisation or convex-concave minimax problems and propose a novel algorithm that uses only one gradient/operator evaluation and one…

Optimization and Control · Mathematics 2023-07-24 Michael Sedlmayer , Dang-Khoa Nguyen , Radu Ioan Bot

We consider a composite convex minimization problem associated with regularized empirical risk minimization, which often arises in machine learning. We propose two new stochastic gradient methods that are based on stochastic dual averaging…

Optimization and Control · Mathematics 2016-03-09 Tomoya Murata , Taiji Suzuki

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…

Optimization and Control · Mathematics 2020-10-27 Quoc Tran-Dinh , Deyi Liu , Lam M. Nguyen

This paper is devoted to the variational inequality problems. We consider two classes of problems, the first is classical constrained variational inequality and the second is the same problem with functional (inequality type) constraints.…

Optimization and Control · Mathematics 2025-06-04 Mohammad S. Alkousa , Belal A. Alashqar , Fedor S. Stonyakin , Tarek Nabhani , Seydamet S. Ablaev

The article is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Starting from the recently proposed proximal variant of the extragradient method for this class…

Optimization and Control · Mathematics 2023-08-02 S. S. Ablaev , F. S. Stonyakin , M. S. Alkousa , D. A. Pasechnyuk

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators…

Machine Learning · Computer Science 2019-02-06 Francis Bach , Kfir Y. Levy

We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…

Optimization and Control · Mathematics 2022-11-08 Ningning Han , Juan Nie , Jian Lu , Michael K. Ng

Stochastic optimization algorithms with variance reduction have proven successful for minimizing large finite sums of functions. Unfortunately, these techniques are unable to deal with stochastic perturbations of input data, induced for…

Machine Learning · Statistics 2017-11-16 Alberto Bietti , Julien Mairal

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…

Optimization and Control · Mathematics 2023-05-26 Hui Ouyang

In this paper we consider the variable inequality problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical system…

Optimization and Control · Mathematics 2014-09-10 J. Y. Bello Cruz , L. R. Lucambio Perez , G. Bouza Allende

Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…

Optimization and Control · Mathematics 2023-03-24 Runchao Ma , Qihang Lin , Tianbao Yang

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a…

Optimization and Control · Mathematics 2015-09-10 Yuchen Zhang , Lin Xiao

Stochastic methods for minimizing a convex integral functional, as initiated by Robbins and Monro in the early 1950s, rely on the evaluation of a gradient (or subgradient if the function is not smooth) and moving in the corresponding…

Optimization and Control · Mathematics 2016-05-12 Miroslav Bacak

This paper presents a proximal-point-based catalyst scheme for simple first-order methods applied to convex minimization and convex-concave minimax problems. In particular, for smooth and (strongly)-convex minimization problems, the…

Optimization and Control · Mathematics 2023-11-09 Guanghui Lan , Yan Li

We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…

Machine Learning · Computer Science 2017-12-27 Xingguo Li , Raman Arora , Han Liu , Jarvis Haupt , Tuo Zhao

This paper provides a unifying theoretical framework for stochastic optimization algorithms by means of a latent stochastic variational problem. Using techniques from stochastic control, the solution to the variational problem is shown to…

Machine Learning · Computer Science 2019-10-29 Philippe Casgrain

In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties.…

Optimization and Control · Mathematics 2024-08-07 Cheik Traoré , Vassilis Apidopoulos , Saverio Salzo , Silvia Villa

In the paper, we generalize the approach Gasnikov et. al, 2017, which allows to solve (stochastic) convex optimization problems with an inexact gradient-free oracle, to the convex-concave saddle-point problem. The proposed approach works,…

Optimization and Control · Mathematics 2022-09-13 Aleksandr Beznosikov , Abdurakhmon Sadiev , Alexander Gasnikov