  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.
