相关论文: Decentralized Langevin Dynamics
We analyze a recently proposed class of algorithms for the problem of sampling from probability distributions $\mu^\ast$ in $\mathbb{R}^d$ with a Lebesgue density of the form $\mu^\ast(x) \propto \exp(-f(Kx)-g(x))$, where $K$ is a linear…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
Markov chain Monte Carlo samplers based on discretizations of (overdamped) Langevin dynamics are commonly used in the Bayesian inference and computational statistical physics literature to estimate high-dimensional integrals. One can…
Langevin dynamics are widely used in sampling high-dimensional, non-Gaussian distributions whose densities are known up to a normalizing constant. In particular, there is strong interest in unadjusted Langevin algorithms (ULA), which…
Despite having various attractive qualities such as high prediction accuracy and the ability to quantify uncertainty and avoid over-fitting, Bayesian Matrix Factorization has not been widely adopted because of the prohibitive cost of…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
The randomized midpoint Langevin Monte Carlo (RLMC), introduced by Shen and Lee (2019), is a variant of classical Unadjusted Langevin Algorithm. It was shown in the literature that the RLMC is an efficient algorithm for approximating…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
This paper proposes a novel family of primal-dual-based distributed algorithms for smooth, convex, multi-agent optimization over networks that uses only gradient information and gossip communications. The algorithms can also employ…
Decentralized distributed optimization over time-varying graphs (networks) is nowadays a very popular branch of research in optimization theory and consensus theory. One of the motivations to consider such networks is an application to…
We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…
Probably one of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al.…
We study the problem of sampling from strongly log-concave distributions over $\mathbb{R}^d$ using the Poisson midpoint discretization (a variant of the randomized midpoint method) for overdamped/underdamped Langevin dynamics. We prove its…
The discretization of overdamped Langevin dynamics, through schemes such as the Euler-Maruyama method, can be corrected by some acceptance/rejection rule, based on a Metropolis-Hastings criterion for instance. In this case, the invariant…
We study non-convex distributed optimization problems where a set of agents collaboratively solve a separable optimization problem that is distributed over a time-varying network. The existing methods to solve these problems rely on (at…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
Recent advances in stochastic gradient techniques have made it possible to estimate posterior distributions from large datasets via Markov Chain Monte Carlo (MCMC). However, when the target posterior is multimodal, mixing performance is…
Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In…
Langevin algorithms are popular Markov chain Monte Carlo methods that are often used to solve high-dimensional large-scale sampling problems in machine learning. The most classical Langevin Monte Carlo algorithm is based on the overdamped…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized…