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Related papers: Mirror Descent-Type Algorithms for the Variational…

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In this paper we propose new algorithms for solving a class of structured monotone variational inequality (VI) problems over compact feasible sets. By identifying the gradient components existing in the operator of VI, we show that it is…

Optimization and Control · Mathematics 2021-11-02 Guanghui Lan , Yuyuan Ouyang

Safety is an essential requirement for reinforcement learning systems. The newly emerging framework of robust constrained Markov decision processes allows learning policies that satisfy long-term constraints while providing guarantees under…

Machine Learning · Computer Science 2025-12-19 David M. Bossens , Atsushi Nitanda

We investigate different randomizations for mirror descent method. We try to propose such a randomization that allows us to use sparsity of the problem as much as it possible. In the paper one can also find a generalization of randomizaed…

Optimization and Control · Mathematics 2016-12-12 Anton Anikin , Alexander Gasnikov , Alexander Gornov

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

Optimization and Control · Mathematics 2019-07-18 Mostafa Amini , Farzad Yousefian

In this paper we consider non-smooth convex optimization problems with (possibly) infinite intersection of constraints. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets,…

Optimization and Control · Mathematics 2024-01-11 Angelia Nedich , Ion Necoara

This paper explores a new framework for reinforcement learning based on online convex optimization, in particular mirror descent and related algorithms. Mirror descent can be viewed as an enhanced gradient method, particularly suited to…

Machine Learning · Computer Science 2012-10-19 Sridhar Mahadevan , Bo Liu

This paper studies the convergence of the mirror descent algorithm for finite horizon stochastic control problems with measure-valued control processes. The control objective involves a convex regularisation function, denoted as $h$, with…

Optimization and Control · Mathematics 2025-08-22 Bekzhan Kerimkulov , David Šiška , Łukasz Szpruch , Yufei Zhang

Some adaptive analogue of the Mirror Prox method for variational inequalities is proposed. In this work we consider the adaptation not only to the value of the Lipschitz constant, but also to the magnitude of the oracle error. This…

Optimization and Control · Mathematics 2020-03-27 Fedor Stonyakin , Evgeniya Vorontsova , Mohammad Alkousa

Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…

Optimization and Control · Mathematics 2025-03-24 Liang Zhang , Niao He , Michael Muehlebach

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a…

Optimization and Control · Mathematics 2018-03-26 Yu. Malitsky

We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…

Optimization and Control · Mathematics 2022-06-14 Ahmet Alacaoglu , Yura Malitsky

The paper investigates two inertial extragradient algorithms for seeking a common solution to a variational inequality problem involving a monotone and Lipschitz continuous mapping and a fixed point problem with a demicontractive mapping in…

Optimization and Control · Mathematics 2023-08-08 Bing Tan , Liya Liu , Xiaolong Qin

We develop a new proximal-gradient method for minimizing the sum of a differentiable, possibly nonconvex, function plus a convex, possibly non differentiable, function. The key features of the proposed method are the definition of a…

Numerical Analysis · Mathematics 2016-05-13 Silvia Bonettini , Ignace Loris , Federica Porta , Marco Prato

This paper establishes the convergence properties of the Popov mirror-prox algorithm for solving stochastic and deterministic variational inequalities (VIs) under a polynomial growth condition on the mapping variation. Unlike existing…

Optimization and Control · Mathematics 2025-10-21 Abhishek Chakraborty , Angelia Nedić

Recently there has been renewed interests in derivative free approaches to stochastic optimization. In this paper, we examine the rates of convergence for the Kiefer-Wolfowitz algorithm and the mirror descent algorithm, under various…

Optimization and Control · Mathematics 2016-10-31 Liyi Dai

Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around…

It is well known that mirror descent may diverge or cycle on merely monotone variational inequalities. In this paper, we propose \emph{Target Mirror Descent} (TMD), a unified framework that stabilizes monotone flows via a target point…

Optimization and Control · Mathematics 2026-04-22 Yu-Wen Chen , Can Kizilkale , Murat Arcak

We study the problem of differentially-private (DP) stochastic (convex-concave) saddle-points in the $\ell_1$ setting. We propose $(\varepsilon, \delta)$-DP algorithms based on stochastic mirror descent that attain nearly…

Optimization and Control · Mathematics 2025-11-17 Tomás González , Cristóbal Guzmán , Courtney Paquette

We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…

Optimization and Control · Mathematics 2017-05-02 Saverio Salzo

The part of the analysis of the convergence rate of the mirror descent method that is connected with the adaptive time-varying step size rules due to Alkousa et al. (MOTOR 2024, pp. 3-18) is corrected. Moreover, a Lipschitz-free mirror…

Optimization and Control · Mathematics 2025-06-03 Bowen Yuan , Mohammad S. Alkousa