Nearly-sharp comparative analyses of related MCMC algorithms

Prove nearly-matching upper and lower bounds that enable rigorous performance comparisons between pairs of similar MCMC algorithms—particularly among gradient-based and stochastic-gradient methods—demonstrating under reasonable assumptions when one algorithm provably outperforms another.

Background

The authors point out that despite the popularity of gradient and stochastic-gradient methods, existing theoretical results are generally too imprecise to support strong algorithm-to-algorithm comparisons or hyperparameter tuning.

They explicitly frame this deficiency as giving rise to many open problems, inviting work that establishes nearly-sharp comparisons to determine when one method is demonstrably superior.