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This paper revisits the convergence of Stochastic Mirror Descent (SMD) in the contemporary nonconvex optimization setting. Existing results for batch-free nonconvex SMD restrict the choice of the distance generating function (DGF) to be…

Optimization and Control · Mathematics 2024-02-28 Ilyas Fatkhullin , Niao He

The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…

Optimization and Control · Mathematics 2021-02-25 Shixiang Chen , Alfredo Garcia , Shahin Shahrampour

The minimax excess risk optimization (MERO) problem is a new variation of the traditional distributionally robust optimization (DRO) problem, which achieves uniformly low regret across all test distributions under suitable conditions. In…

Optimization and Control · Mathematics 2024-08-23 Zhihao Gu , Zi Xu

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…

We investigate the distributed online nonconvex optimization problem with differential privacy over time-varying networks. Each node minimizes the sum of several nonconvex functions while preserving the node's differential privacy. We…

Systems and Control · Electrical Eng. & Systems 2025-01-09 Yingjie Zhou , Tao Li

The time to converge to the steady state of a finite Markov chain can be greatly reduced by a lifting operation, which creates a new Markov chain on an expanded state space. For a class of quadratic objectives, we show an analogous behavior…

Machine Learning · Statistics 2017-03-14 Guilherme França , José Bento

Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…

Optimization and Control · Mathematics 2025-03-26 David Shirokoff , Philip Zaleski

To solve distributed optimization efficiently with various constraints and nonsmooth functions, we propose a distributed mirror descent algorithm with embedded Bregman damping, as a generalization of conventional distributed…

Optimization and Control · Mathematics 2021-08-30 Guanpu Chen , Weijian Li , Gehui Xu , Yiguang Hong

We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…

Optimization and Control · Mathematics 2019-05-28 Lukáš Adam , Martin Branda

An open problem in optimization with noisy information is the computation of an exact minimizer that is independent of the amount of noise. A standard practice in stochastic approximation algorithms is to use a decreasing step-size. This…

Optimization and Control · Mathematics 2021-02-24 Anastasia Borovykh , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…

Computation · Statistics 2025-11-07 Francesca R. Crucinio

Motivated by broad applications in machine learning, we study the popular accelerated stochastic gradient descent (ASGD) algorithm for solving (possibly nonconvex) optimization problems. We characterize the finite-time performance of this…

Optimization and Control · Mathematics 2020-10-20 Thinh T. Doan , Lam M. Nguyen , Nhan H. Pham , Justin Romberg

Motivated by broad applications in reinforcement learning and machine learning, this paper considers the popular stochastic gradient descent (SGD) when the gradients of the underlying objective function are sampled from Markov processes.…

Optimization and Control · Mathematics 2020-04-02 Thinh T. Doan , Lam M. Nguyen , Nhan H. Pham , Justin Romberg

This paper deals with distributed optimization problems that use compressed communication to achieve efficient performance and mitigate communication bottleneck. We propose a family of compression schemes in which operators transform…

Optimization and Control · Mathematics 2026-01-13 Andrey Veprikov , Vladimir Solodkin , Mikhail Rudakov , Petr Babkin , Aleksandr Beznosikov

Many problems in machine learning can be formulated as optimizing a convex functional over a vector space of measures. This paper studies the convergence of the mirror descent algorithm in this infinite-dimensional setting. Defining Bregman…

Optimization and Control · Mathematics 2022-10-12 Pierre-Cyril Aubin-Frankowski , Anna Korba , Flavien Léger

Learning-to-optimize is an emerging framework that seeks to speed up the solution of certain optimization problems by leveraging training data. Learned optimization solvers have been shown to outperform classical optimization algorithms in…

Optimization and Control · Mathematics 2023-02-27 Hong Ye Tan , Subhadip Mukherjee , Junqi Tang , Carola-Bibiane Schönlieb

In this paper, we consider an online distributed composite optimization problem over a time-varying multi-agent network that consists of multiple interacting nodes, where the objective function of each node consists of two parts: a loss…

Optimization and Control · Mathematics 2020-04-03 Deming Yuan , Yiguang Hong , Daniel W. C. Ho , Shengyuan Xu

In the paper we consider an application of mirror descent (dual averaging) to the stochastic online convex optimization problems. We compare classical mirror descent (Nemirovski-Yudin, 1979) with dual averaging (Nesterov, 2005) and…

Optimization and Control · Mathematics 2016-12-12 Alexander Gasnikov , Yurii Nesterov , Vladimir Spokoiny

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

Optimization and Control · Mathematics 2024-11-06 Kexin Jin , Jonas Latz , Chenguang Liu , Alessandro Scagliotti

We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.

Optimization and Control · Mathematics 2017-08-01 Anastasia Bayandina , Alexander Gasnikov , Evgenia Gasnikova , Sergey Matsievsky