Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMC

TL;DR

This paper introduces a bandit-based method for automatically tuning hyperparameters in stochastic gradient MCMC algorithms, improving their accuracy and practicality for Bayesian inference.

Contribution

It proposes a novel Stein discrepancy-based tuning algorithm supported by theoretical analysis and extensive experiments, addressing the lack of automated hyperparameter tuning in SGMCMC.

Findings

The method effectively tunes hyperparameters across various datasets.

It reduces the need for manual hyperparameter tuning.

Experimental results show improved posterior approximation accuracy.

Abstract

Stochastic gradient Markov chain Monte Carlo (SGMCMC) is a popular class of algorithms for scalable Bayesian inference. However, these algorithms include hyperparameters such as step size or batch size that influence the accuracy of estimators based on the obtained posterior samples. As a result, these hyperparameters must be tuned by the practitioner and currently no principled and automated way to tune them exists. Standard MCMC tuning methods based on acceptance rates cannot be used for SGMCMC, thus requiring alternative tools and diagnostics. We propose a novel bandit-based algorithm that tunes the SGMCMC hyperparameters by minimizing the Stein discrepancy between the true posterior and its Monte Carlo approximation. We provide theoretical results supporting this approach and assess various Stein-based discrepancies. We support our results with experiments on both simulated and real datasets, and find that this method is practical for a wide range of applications.