Robust Approximate Sampling via Stochastic Gradient Barker Dynamics

TL;DR

This paper introduces the stochastic gradient Barker dynamics (SGBD), a robust MCMC algorithm for Bayesian sampling that effectively handles gradient noise and hyperparameter sensitivity, outperforming Langevin-based methods in high-dimensional settings.

Contribution

The paper develops SGBD, extending Barker MCMC to stochastic gradients, with a bias correction mechanism that reduces gradient noise impact and enhances robustness.

Findings

SGBD outperforms Langevin dynamics in high-dimensional experiments.

SGBD is more robust to hyperparameter choices and gradient irregularities.

The bias correction eliminates gradient noise errors under certain conditions.

Abstract

Stochastic Gradient (SG) Markov Chain Monte Carlo algorithms (MCMC) are popular algorithms for Bayesian sampling in the presence of large datasets. However, they come with little theoretical guarantees and assessing their empirical performances is non-trivial. In such context, it is crucial to develop algorithms that are robust to the choice of hyperparameters and to gradients heterogeneity since, in practice, both the choice of step-size and behaviour of target gradients induce hard-to-control biases in the invariant distribution. In this work we introduce the stochastic gradient Barker dynamics (SGBD) algorithm, extending the recently developed Barker MCMC scheme, a robust alternative to Langevin-based sampling algorithms, to the stochastic gradient framework. We characterize the impact of stochastic gradients on the Barker transition mechanism and develop a bias-corrected version that, under suitable assumptions, eliminates the error due to the gradient noise in the proposal. We illustrate the performance on a number of high-dimensional examples, showing that SGBD is more robust to hyperparameter tuning and to irregular behavior of the target gradients compared to the popular stochastic gradient Langevin dynamics algorithm.