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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

Motivated by neural network training in finite-precision arithmetic environments, this work studies the convergence of perturbed iterate SGD using adaptive step sizes in an environment with numerical error. Considering a general stochastic…

Optimization and Control · Mathematics 2025-09-10 Michael R. Metel

We provide novel information-theoretic generalization bounds for stochastic gradient Langevin dynamics (SGLD) under the assumptions of smoothness and dissipativity, which are widely used in sampling and non-convex optimization studies. Our…

Machine Learning · Computer Science 2023-11-03 Futoshi Futami , Masahiro Fujisawa

Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too…

Machine Learning · Computer Science 2024-06-04 Haoyang Zheng , Hengrong Du , Qi Feng , Wei Deng , Guang Lin

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

Machine Learning · Computer Science 2025-12-09 Hongjian Lan , Yucong Liu , Florian Schäfer

This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…

Optimization and Control · Mathematics 2025-05-21 Nahom Seyoum , Haoxiang You

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…

Machine Learning · Statistics 2025-09-09 Junhua Chen , Lorenz Richter , Julius Berner , Denis Blessing , Gerhard Neumann , Anima Anandkumar

The viability of a variant of numerical stochastic perturbation theory, where the Langevin equation is replaced by the SMD algorithm, is examined. In particular, the convergence of the process to a unique stationary state is rigorously…

High Energy Physics - Lattice · Physics 2017-06-02 Mattia Dalla Brida , Martin Lüscher

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Machine Learning · Statistics 2015-09-08 David A. Knowles

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…

Machine Learning · Computer Science 2024-03-14 Alex Damian , Loucas Pillaud-Vivien , Jason D. Lee , Joan Bruna

We develop a framework that allows the use of the multi-level Monte Carlo (MLMC) methodology (Giles2015) to calculate expectations with respect to the invariant measure of an ergodic SDE. In that context, we study the (over-damped) Langevin…

Numerical Analysis · Mathematics 2019-08-13 Michael B. Giles , Mateusz B. Majka , Lukasz Szpruch , Sebastian Vollmer , Konstantinos Zygalakis

The current interpretation of stochastic gradient descent (SGD) as a stochastic process lacks generality in that its numerical scheme restricts continuous-time dynamics as well as the loss function and the distribution of gradient noise. We…

Machine Learning · Statistics 2019-11-21 Soma Yokoi , Issei Sato

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models…

Machine Learning · Statistics 2017-06-16 Yi-An Ma , Nicholas J. Foti , Emily B. Fox

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization and Control · Mathematics 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

Stochastic Gradient Descent (SGD) is a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…

Optimization and Control · Mathematics 2021-04-02 Vivak Patel , Shushu Zhang

In many applications involving large dataset or online updating, stochastic gradient descent (SGD) provides a scalable way to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory…

Machine Learning · Statistics 2017-07-04 Yixin Fang , Jinfeng Xu , Lei Yang

We propose a stochastic gradient Markov chain Monte Carlo (SG-MCMC) algorithm for scalable inference in mixed-membership stochastic blockmodels (MMSB). Our algorithm is based on the stochastic gradient Riemannian Langevin sampler and…

Machine Learning · Computer Science 2015-10-23 Wenzhe Li , Sungjin Ahn , Max Welling

Stochastic Gradient Langevin Dynamics infuses isotropic gradient noise to SGD to help navigate pathological curvature in the loss landscape for deep networks. Isotropic nature of the noise leads to poor scaling, and adaptive methods based…

Machine Learning · Computer Science 2019-06-13 Chandrasekaran Anirudh Bhardwaj

Non-gaussian spatial data are very common in many disciplines. For instance, count data are common in disease mapping, and binary data are common in ecology. When fitting spatial regressions for such data, one needs to account for…

Methodology · Statistics 2010-12-01 John Hughes , Murali Haran

A framework is introduced for solving a sequence of slowly changing optimization problems, including those arising in regression and classification applications, using optimization algorithms such as stochastic gradient descent (SGD). The…

Machine Learning · Computer Science 2015-09-25 Craig Wilson , Venugopal V. Veeravalli