Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates

05/28/2019
by   Adil Salim, et al.
0

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth term and multiple stochastic nonsmooth terms. In each iteration, our splitting technique only requires access to a stochastic gradient of the smooth term and a stochastic proximal operator for each of the nonsmooth terms. We establish nonasymptotic sublinear and linear convergence rates under convexity and strong convexity of the smooth term, respectively, expressed in terms of the KL divergence and Wasserstein distance. We illustrate the efficiency of our sampling technique through numerical simulations on a Bayesian learning task.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
12/04/2019

Stochastic proximal splitting algorithm for stochastic composite minimization

Supported by the recent contributions in multiple branches, the first-or...
research
06/16/2020

Primal Dual Interpretation of the Proximal Stochastic Gradient Langevin Algorithm

We consider the task of sampling with respect to a log concave probabili...
research
01/31/2016

A Proximal Stochastic Quasi-Newton Algorithm

In this paper, we discuss the problem of minimizing the sum of two conve...
research
04/03/2020

Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms

We introduce a new primal-dual algorithm for minimizing the sum of three...
research
10/21/2022

The Stochastic Proximal Distance Algorithm

Stochastic versions of proximal methods have gained much attention in st...
research
04/10/2023

Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Space

Variational inference (VI) seeks to approximate a target distribution π ...
research
04/07/2021

Time-Data Tradeoffs in Structured Signals Recovery via Proximal-Gradient Homotopy Method

In this paper, we characterize data-time tradeoffs of the proximal-gradi...

Please sign up or login with your details

Forgot password? Click here to reset