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Related papers: Adaptive stepsize algorithms for Langevin dynamics

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Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Machine Learning · Computer Science 2020-11-03 Xavier Alameda-Pineda , Vincent Drouard , Radu Horaud

We propose and analyze an adaptive step-size variant of the Davis-Yin three operator splitting. This method can solve optimization problems composed by a sum of a smooth term for which we have access to its gradient and an arbitrary number…

Optimization and Control · Mathematics 2018-08-02 Fabian Pedregosa , Gauthier Gidel

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

Probability · Mathematics 2023-08-10 Anatolii A. Puhalskii

The Newton method is a powerful optimization algorithm, valued for its rapid local convergence and elegant geometric properties. However, its theoretical guarantees are usually limited to convex problems. In this work, we ask whether…

Optimization and Control · Mathematics 2025-10-01 Alexander Shestakov , Sushil Bohara , Samuel Horváth , Martin Takáč , Slavomír Hanzely

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as…

Machine Learning · Computer Science 2025-02-12 Chanyeong Kim , Jongwoong Park , Hyunglip Bae , Woo Chang Kim

The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain. The simulations of this stochastic process and its invariant measure are…

Numerical Analysis · Mathematics 2025-05-20 Dawei Wu , Zhennan Zhou

Score-based diffusion methods provide a powerful strategy to solve image restoration tasks by flexibly combining a pre-trained foundational prior model with a likelihood function specified during test time. Such methods are predominantly…

Computer Vision and Pattern Recognition · Computer Science 2024-09-09 Charlesquin Kemajou Mbakam , Jean-Francois Giovannelli , Marcelo Pereyra

For parabolic stochastic partial differential equations (SPDEs), we show that the numerical methods, including the spatial spectral Galerkin method and further the full discretization via the temporal accelerated exponential Euler method,…

Numerical Analysis · Mathematics 2021-06-22 Chuchu Chen , Ziheng Chen , Jialin Hong , Diancong Jin

Discretizations of Langevin diffusions provide a powerful method for sampling and Bayesian inference. However, such discretizations require evaluation of the gradient of the potential function. In several real-world scenarios, obtaining…

Statistics Theory · Mathematics 2021-01-19 Abhishek Roy , Lingqing Shen , Krishnakumar Balasubramanian , Saeed Ghadimi

In this paper, we suggest a new framework for analyzing primal subgradient methods for nonsmooth convex optimization problems. We show that the classical step-size rules, based on normalization of subgradient, or on the knowledge of optimal…

Optimization and Control · Mathematics 2023-11-27 Yurii Nesterov

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and…

Machine Learning · Computer Science 2023-01-31 Junlong Lyu , Zhitang Chen , Wenlong Lyu , Jianye Hao

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted…

Numerical Analysis · Mathematics 2022-12-23 Martin Eigel , Robert Gruhlke , David Sommer

D. B. Br\"{u}ckner et al. [Phys. Rev. Lett. 125, 058103 (2020)] have described a novel method for inferring the dynamics of systems governed by an underdamped Langevin equation in the presence of measurement noise. While this is a…

Statistical Mechanics · Physics 2026-04-10 Yeeren I. Low

For sampling from a log-concave density, we study implicit integrators resulting from $\theta$-method discretization of the overdamped Langevin diffusion stochastic differential equation. Theoretical and algorithmic properties of the…

Machine Learning · Statistics 2021-07-13 Liam Hodgkinson , Robert Salomone , Fred Roosta

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…

Statistical Mechanics · Physics 2007-12-03 Vivien Lecomte , Julien Tailleur

Approximate dynamic programming (ADP) has proven itself in a wide range of applications spanning large-scale transportation problems, health care, revenue management, and energy systems. The design of effective ADP algorithms has many…

Optimization and Control · Mathematics 2014-07-15 Ilya O. Ryzhov , Peter I. Frazier , Warren B. Powell

A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are…

Strongly Correlated Electrons · Physics 2022-05-31 Francisco Meirinhos , Michael Kajan , Johann Kroha , Tim Bode

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

Machine Learning · Computer Science 2021-07-16 Vyacheslav Kungurtsev , Adam Cobb , Tara Javidi , Brian Jalaian

We introduce a numerical method for Brownian dynamics with position dependent diffusion tensor which is second order accurate for sampling the invariant measure while requiring only one force evaluation per timestep. Analysis of the…

Numerical Analysis · Mathematics 2025-01-09 Eugen Bronasco , Benedict Leimkuhler , Dominic Phillips , Gilles Vilmart

We consider the problem of sampling from an unknown distribution for which only a sufficiently large number of training samples are available. Such settings have recently drawn considerable interest in the context of generative modelling…

Machine Learning · Statistics 2024-10-24 Georg A. Gottwald , Fengyi Li , Youssef Marzouk , Sebastian Reich