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 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 SGMCMC hyperparameters to maximize the accuracy of the posterior approximation by minimizing the kernel Stein discrepancy (KSD). We provide theoretical results supporting this approach and assess alternative metrics to KSD. We support our results with experiments on both simulated and real datasets, and find that this method is practical for a wide range of application areas.