Learning to Explore for Stochastic Gradient MCMC

Bayesian Neural Networks (BNNs) with highdimensional parameters pose a challenge for posterior inference due to the multi-modality of the posterior distributions. Stochastic Gradient Markov Chain Monte Carlo (SGMCMC) with cyclical learning rate scheduling is a promising solution, but it requires a large number of sampling steps to explore high-dimensional multimodal posteriors, making it computationally expensive. In this paper, we propose a metalearning strategy to build SGMCMC which can efficiently explore the multi-modal target distributions. Our algorithm allows the learned SGM-CMC to quickly explore the high-density region of the posterior landscape. Also, we show that this exploration property is transferrable to various tasks, even for the ones unseen during a meta-training stage. Using popular image classification benchmarks and a variety of downstream tasks, we demonstrate that our method significantly improves the sampling efficiency, achieving better performance than vanilla SGM-CMC without incurring significant computational overhead.