Efficient and Generalizable Tuning Strategies for Stochastic Gradient MCMC
This addresses a bottleneck for practitioners in scalable Bayesian inference by providing an automated tuning method, though it is incremental as it builds on existing SGMCMC frameworks.
The paper tackles the problem of tuning hyperparameters in stochastic gradient MCMC (SGMCMC) algorithms, which lack automated methods, by proposing a bandit-based algorithm that minimizes Stein discrepancy to improve posterior approximation accuracy, achieving practical results on simulated and real datasets.
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.