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This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…

Optimization and Control · Mathematics 2013-07-09 Angelia Nedich , Soomin Lee

Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for…

Optimization and Control · Mathematics 2024-11-13 Jian Chen , Liping Tang , Xinmin Yang

We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…

Machine Learning · Statistics 2026-05-26 Mohammadreza Ahmadypour , Tara Javidi , Farinaz Koushanfar

This letter investigates the convergence and concentration properties of the Stochastic Mirror Descent (SMD) algorithm utilizing biased stochastic subgradients. We establish the almost sure convergence of the algorithm's iterates under the…

Optimization and Control · Mathematics 2024-07-09 Anik Kumar Paul , Arun D Mahindrakar , Rachel K Kalaimani

In this work we propose MirrorCBO, a consensus-based optimization (CBO) method which generalizes standard CBO in the same way that mirror descent generalizes gradient descent. For this we apply the CBO methodology to a swarm of dual…

Optimization and Control · Mathematics 2025-07-17 Leon Bungert , Franca Hoffmann , Dohyeon Kim , Tim Roith

Machine learning problems with multiple objective functions appear either in learning with multiple criteria where learning has to make a trade-off between multiple performance metrics such as fairness, safety and accuracy; or, in…

Machine Learning · Computer Science 2024-03-20 Heshan Fernando , Han Shen , Miao Liu , Subhajit Chaudhury , Keerthiram Murugesan , Tianyi Chen

We investigate Stochastic Mirror Descent (SMD) with matrix parameters and vector-valued predictions, a framework relevant to multi-class classification and matrix completion problems. Focusing on the overparameterized regime, where the…

Machine Learning · Statistics 2026-03-02 Danil Akhtiamov , Reza Ghane , Omead Pooladzandi , Babak Hassibi

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

Optimization and Control · Mathematics 2022-06-02 Wang Chen , Xinmin Yang , Yong Zhao

We investigate the convergence of stochastic mirror descent (SMD) under interpolation in relatively smooth and smooth convex optimization. In relatively smooth convex optimization we provide new convergence guarantees for SMD with a…

Optimization and Control · Mathematics 2023-05-26 Ryan D'Orazio , Nicolas Loizou , Issam Laradji , Ioannis Mitliagkas

Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on Riemannian…

Machine Learning · Statistics 2026-03-19 Jiaxin Jiang , Lei Shi , Jiyuan Tan

Value iteration-type methods have been extensively studied for computing a nearly optimal value function in reinforcement learning (RL). Under a generative sampling model, these methods can achieve sharper sample complexity than policy…

Optimization and Control · Mathematics 2026-04-08 Zhichao Jia , Guanghui Lan

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

Sampling from an unnormalized target distribution is an essential problem with many applications in probabilistic inference. Stein Variational Gradient Descent (SVGD) has been shown to be a powerful method that iteratively updates a set of…

Machine Learning · Computer Science 2023-02-13 Hoang Phan , Ngoc Tran , Trung Le , Toan Tran , Nhat Ho , Dinh Phung

In machine learning and statistical data analysis, we often run into objective function that is a summation: the number of terms in the summation possibly is equal to the sample size, which can be enormous. In such a setting, the stochastic…

Machine Learning · Statistics 2022-08-30 Yiling Luo , Xiaoming Huo , Yajun Mei

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

Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we…

Optimization and Control · Mathematics 2020-06-19 Florian Schäfer , Anima Anandkumar , Houman Owhadi

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 mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…

Optimization and Control · Mathematics 2024-03-13 Anastasia Borovykh , Nikolas Kantas , Panos Parpas , Grigorios A. Pavliotis

We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…

Optimization and Control · Mathematics 2024-06-24 Morteza Maleknia , Majid Soleimani-damaneh

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