Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SG-MCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key components: i) adaptive preconditioners (as in ADAgrad or RMSprop), and ii) adaptive element-wise momentum weights. The zero-temperature limit gives a novel stochastic optimization method with adaptive element-wise momentum weights, while conventional optimization methods only have a shared, static momentum weight. Under certain assumptions, our theoretical analysis suggests the proposed simulated annealing approach converges close to the global optima. Experiments on several deep neural network models show state-of-the-art results compared to related stochastic optimization algorithms.