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Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose…

Machine Learning · Statistics 2025-08-29 Facheng Yu , Ronak Mehta , Alex Luedtke , Zaid Harchaoui

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

Probability · Mathematics 2007-05-23 Clive G. Wells

Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical…

Optimization and Control · Mathematics 2023-09-06 Stefano Di Giovacchino , Desmond J. Higham , Konstantinos Zygalakis

Consider linear ill-posed problems governed by the system $A_i x = y_i$ for $i =1, \cdots, p$, where each $A_i$ is a bounded linear operator from a Banach space $X$ to a Hilbert space $Y_i$. In case $p$ is huge, solving the problem by an…

Numerical Analysis · Mathematics 2023-05-17 Qinian Jin , Xiliang Lu , Liuying Zhang

Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…

Optimization and Control · Mathematics 2026-04-10 Qing Xu , Yiwei Liao , Wenqi Fan , Xingxing You , Songyi Dian

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation…

Optimization and Control · Mathematics 2024-05-31 Siming Liang , Hui Sun , Richard Archibald , Feng Bao

In many learning settings, it is beneficial to augment the main features with pairwise interactions. Such interaction models can be often enhanced by performing variable selection under the so-called strong hierarchy constraint: an…

Machine Learning · Statistics 2020-07-15 Hussein Hazimeh , Rahul Mazumder

Decentralized stochastic optimization is the basic building block of modern collaborative machine learning, distributed estimation and control, and large-scale sensing. Since involved data usually contain sensitive information like user…

Machine Learning · Computer Science 2022-05-10 Yongqiang Wang , H. Vincent Poor

This paper considers a stochastic approximation algorithm, with decreasing step size and martingale difference noise. Under very mild assumptions, we prove the non convergence of this process toward a certain class of repulsive sets for the…

Probability · Mathematics 2010-01-28 Michel Benaïm , Mathieu Faure

We study discrete-time mirror descent applied to the unregularized empirical risk in matrix sensing. In both the general case of rectangular matrices and the particular case of positive semidefinite matrices, a simple potential-based…

Machine Learning · Statistics 2021-10-28 Fan Wu , Patrick Rebeschini

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…

Machine Learning · Computer Science 2022-10-21 Alberto Lanconelli , Christopher S. A. Lauria

In this paper, we consider a distributed constrained optimization problem with delayed subgradient information over the time-varying communication network, where each agent can only communicate with its neighbors and the communication…

Optimization and Control · Mathematics 2021-06-16 Jie Liu , Zhan Yu , Daniel W. C. Ho

Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…

Statistics Theory · Mathematics 2024-04-16 Cecile Durot , Debarghya Mukherjee

An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…

Statistics Theory · Mathematics 2022-01-12 Antoine Godichon-Baggioni

This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…

Optimization and Control · Mathematics 2020-02-17 Jinlong Lei , Peng Yi , Jie Chen , Yiguang Hong

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…

Machine Learning · Computer Science 2018-09-26 Yao Zhang , Andrew M. Saxe , Madhu S. Advani , Alpha A. Lee

Low-precision training has become crucial for reducing the computational and memory costs of large-scale deep learning. However, quantizing gradients introduces magnitude shrinkage, which can change how stochastic gradient descent (SGD)…

Machine Learning · Computer Science 2026-01-09 Vincent-Daniel Yun

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

Machine Learning · Computer Science 2019-01-21 Navid Azizan , Babak Hassibi

We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be…

Machine Learning · Computer Science 2019-04-23 Hakan Gokcesu , Suleyman S. Kozat

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Statistics Theory · Mathematics 2007-06-13 Anatoli Juditsky , Alexander Nazin , Alexandre Tsybakov , Nicolas Vayatis