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The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on the feasible set is computed, allowing for an appropriate…

Optimization and Control · Mathematics 2021-06-10 Orizon P. Ferreira , Max V. Lemes , Leandro F. Prudente

We present adaptive gradient methods (both basic and accelerated) for solving convex composite optimization problems in which the main part is approximately smooth (a.k.a. $(\delta, L)$-smooth) and can be accessed only via a (potentially…

Optimization and Control · Mathematics 2024-06-11 Anton Rodomanov , Xiaowen Jiang , Sebastian Stich

Learning representation from relative similarity comparisons, often called ordinal embedding, gains rising attention in recent years. Most of the existing methods are based on semi-definite programming (\textit{SDP}), which is generally…

Machine Learning · Computer Science 2019-12-03 Ke Ma , Jinshan Zeng , Qianqian Xu , Xiaochun Cao , Wei Liu , Yuan Yao

Improved rates of convergence for ergodic homogeneous Markov chains are studied. In comparison to the earlier papers the setting is also generalised to the case without a unique dominated measure. Examples are provided where the new bound…

Probability · Mathematics 2021-11-02 Alexander Veretennikov , Maria Veretennikova

Primal-dual algorithms for the resolution of convex-concave saddle point problems usually come with one or several step size parameters. Within the range where convergence is guaranteed, choosing well the step size can make the difference…

Optimization and Control · Mathematics 2024-03-29 Olivier Fercoq

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the…

Optimization and Control · Mathematics 2018-01-17 Igor Konnov

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…

Machine Learning · Statistics 2018-04-12 Aymeric Dieuleveut , Alain Durmus , Francis Bach

The aim of this paper is to deepen the convergence analysis of the scaled gradient projection (SGP) method, proposed by Bonettini et al. in a recent paper for constrained smooth optimization. The main feature of SGP is the presence of a…

Numerical Analysis · Mathematics 2015-09-10 Silvia Bonettini , Marco Prato

We consider infinite-horizon discounted Markov decision problems with finite state and action spaces and study the convergence rates of the projected policy gradient method and a general class of policy mirror descent methods, all with…

Optimization and Control · Mathematics 2022-03-08 Lin Xiao

This work presents the first finite-time analysis for the last-iterate convergence of average-reward $Q$-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes, which serve as…

Machine Learning · Computer Science 2026-04-07 Zaiwei Chen , Phalguni Nanda

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple…

Optimization and Control · Mathematics 2023-12-29 S. M. Puchinin , E. R. Korolkov , F. S. Stonyakin , M. S. Alkousa , A. A Vyguzov

We analyze the constant step size subgradient method on nonsmooth, nonconvex functions. We identify geometric assumptions on the objective function under which i) its domain admits a partition (stratification) into smooth manifolds (strata)…

Optimization and Control · Mathematics 2026-04-21 Evgenii Chzhen , Sholom Schechtman

The classical convex feasibility problem in a finite dimensional Euclidean space is studied in the present paper. We are interested in two cases. First, we assume to know how to compute an exact project onto one of the sets involved and the…

Optimization and Control · Mathematics 2019-12-10 R. Díaz Millán , O. P. Ferreira , L. F. Prudente

Many popular adaptive gradient methods such as Adam and RMSProp rely on an exponential moving average (EMA) to normalize their stepsizes. While the EMA makes these methods highly responsive to new gradient information, recent research has…

Machine Learning · Computer Science 2021-10-13 Brett Daley , Christopher Amato

This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and…

Optimization and Control · Mathematics 2021-02-02 Zhi Li , Wei Shi , Ming Yan

The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…

Probability · Mathematics 2026-01-21 Alexander Veretennikov

Prescribed-time convergence mechanism has become a prominent research focus in the current field of optimization and control due to its ability to precisely control the target completion time. The recently arisen prescribed-time algorithms…

Optimization and Control · Mathematics 2023-10-31 Shuaiyu Zhou , Yiheng Wei , Jinde Cao , Yang Liu

The Primal-Dual hybrid gradient (PDHG) method is a powerful optimization scheme that breaks complex problems into simple sub-steps. Unfortunately, PDHG methods require the user to choose stepsize parameters, and the speed of convergence is…

Numerical Analysis · Mathematics 2015-03-25 Tom Goldstein , Min Li , Xiaoming Yuan , Ernie Esser , Richard Baraniuk

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient…

Machine Learning · Computer Science 2020-06-02 Liang Liu , Xiaopeng Luo

Adaptive gradient methods like AdaGrad are widely used in optimizing neural networks. Yet, existing convergence guarantees for adaptive gradient methods require either convexity or smoothness, and, in the smooth setting, only guarantee…

Machine Learning · Computer Science 2019-10-22 Xiaoxia Wu , Simon S. Du , Rachel Ward