Related papers: Decentralized Proximal Stochastic Gradient Langevi…
We propose a novel analysis of the Decentralized Stochastic Gradient Descent (DSGD) algorithm with constant step size, interpreting the iterates of the algorithm as a Markov chain. We show that DSGD converges to a stationary distribution,…
In this paper, we provide new insights on the Unadjusted Langevin Algorithm. We show that this method can be formulated as a first order optimization algorithm of an objective functional defined on the Wasserstein space of order $2$. Using…
Exact-sparsity inducing prior distributions in Bayesian analysis typically lead to posterior distributions that are very challenging to handle by standard Markov Chain Monte Carlo (MCMC) methods, particular in high-dimensional models with…
We propose a localized consensus-based method for sampling from non-Gaussian distributions. This method arises from an alternative derivation of consensus-based sampling (CBS). Starting from ensemble-preconditioned Langevin dynamics, we…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…
The use of non-differentiable priors in Bayesian statistics has become increasingly popular, in particular in Bayesian imaging analysis. Current state of the art methods are approximate in the sense that they replace the posterior with a…
Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…
We propose an interacting contour stochastic gradient Langevin dynamics (ICSGLD) sampler, an embarrassingly parallel multiple-chain contour stochastic gradient Langevin dynamics (CSGLD) sampler with efficient interactions. We show that…
Recent research highlights frequent model communication as a significant bottleneck to the efficiency of decentralized machine learning (ML), especially for large-scale and over-parameterized neural networks (NNs). To address this, we…
We study Langevin-type algorithms for sampling from Gibbs distributions such that the potentials are dissipative and their weak gradients have finite moduli of continuity not necessarily convergent to zero. Our main result is a…
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…
Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $\pi(\theta)\propto \exp(-U(\theta)) $, LMC…
It is of significant interest in many applications to sample from a high-dimensional target distribution $\pi$ with the density $\pi(\text{d} x) \propto e^{-U(x)} (\text{d} x) $, based on the temporal discretization of the Langevin…
We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…
The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift, and it naturally arises from the optimization of two-layer neural networks via (noisy) gradient…
This paper proposes a replica exchange preconditioned Langevin diffusion discretized by the Crank-Nicolson scheme (repCNLD) to handle high-dimensional and multi-modal distribution problems. Sampling from high-dimensional and multi-modal…
Recent work has suggested using Monte Carlo methods based on piecewise deterministic Markov processes (PDMPs) to sample from target distributions of interest. PDMPs are non-reversible continuous-time processes endowed with momentum, and…
Motivated by decentralized approaches to machine learning, we propose a collaborative Bayesian learning algorithm taking the form of decentralized Langevin dynamics in a non-convex setting. Our analysis show that the initial KL-divergence…
Sampling from a target distribution is a fundamental problem. Traditional Markov chain Monte Carlo (MCMC) algorithms, such as the unadjusted Langevin algorithm (ULA), derived from the overdamped Langevin dynamics, have been extensively…
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…