Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning

The posteriors over neural network weights are high dimensional and multimodal. Each mode typically characterizes a meaningfully different representation of the data. We develop Cyclical Stochastic Gradient MCMC (SG-MCMC) to automatically explore such distributions. In particular, we propose a cyclical stepsize schedule, where larger steps discover new modes, and smaller steps characterize each mode. We prove that our proposed learning rate schedule provides faster convergence to samples from a stationary distribution than SG-MCMC with standard decaying schedules. Moreover, we provide extensive experimental results to demonstrate the effectiveness of cyclical SG-MCMC in learning complex multimodal distributions, especially for fully Bayesian inference with modern deep neural networks.