Related papers: Taming the Interacting Particle Langevin Algorithm…
Langevin algorithms are gradient descent methods with additive noise. They have been used for decades in Markov chain Monte Carlo (MCMC) sampling, optimization, and learning. Their convergence properties for unconstrained non-convex…
Sampling from constrained statistical distributions is a fundamental task in various fields including Bayesian statistics, computational chemistry, and statistical physics. This article considers the cases where the constrained distribution…
This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…
A growing trend in the database and system communities is to augment conventional index structures, such as B+-trees, with machine learning (ML) models. Among these, error-bounded Piecewise Linear Approximation ($\epsilon$-PLA) has emerged…
This paper is concerned with the design of algorithms based on systems of interacting particles to represent, approximate, and learn the optimal control law for reinforcement learning (RL). The primary contribution is that convergence rates…
In the study of McKean-Vlasov stochastic differential equations (MV-SDEs), numerical approximation plays a crucial role in understanding the behavior of interacting particle systems (IPS). Classical Milstein schemes provide strong…
A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an…
Lagrangian particle tracking is essential for characterizing turbulent flows, but inferring particle acceleration from inherently noisy position data remains a significant challenge. Fluid particles in turbulence experience extreme,…
This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…
Integer Linear Programming (ILP) serves as a versatile framework for modeling a wide range of combinatorial optimization problems, typically addressed by sophisticated exact solvers or heuristics. While learning-based approaches have…
We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include…
Langevin algorithms are gradient descent methods augmented with additive noise, and are widely used in Markov Chain Monte Carlo (MCMC) sampling, optimization, and machine learning. In recent years, the non-asymptotic analysis of Langevin…
In order to solve tasks like uncertainty quantification or hypothesis tests in Bayesian imaging inverse problems, we often have to draw samples from the arising posterior distribution. For the usually log-concave but high-dimensional…
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…
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…
We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as Unadjusted Langevin Algorithm (ULA),…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…
The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis-Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the…