Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization

Changyou Chen; David Carlson; Zhe Gan; Chunyuan Li; Lawrence Carin

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arXiv · 1512.07962

Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization

Changyou Chen·David Carlson·Zhe Gan·Chunyuan Li·Lawrence Carin

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Abstract

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 SGMCMC 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.

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Changyou Chen, David Carlson, Zhe Gan, Chunyuan Li, Lawrence Carin. 2015-12-25. Bridging the Gap between Stochastic Gradient MCMC and Stochastic Optimization. https://arxiv.org/abs/1512.07962

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