Ex^2MCMC: Sampling through Exploration Exploitation
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We develop an Explore-Exploit Markov chain Monte Carlo algorithm (Ex^2MCMC) that combines multiple global proposals and local moves. The proposed method is massively parallelizable and extremely computationally efficient. We prove V-uniform geometric ergodicity of Ex^2MCMC under realistic conditions and compute explicit bounds on the mixing rate showing the improvement brought by the multiple global moves. We show that Ex^2MCMC allows fine-tuning of exploitation (local moves) and exploration (global moves) via a novel approach to proposing dependent global moves. Finally, we develop an adaptive scheme, FlEx^2MCMC, that learns the distribution of global moves using normalizing flows. We illustrate the efficiency of Ex^2MCMC and its adaptive versions on many classical sampling benchmarks. We also show that these algorithms improve the quality of sampling GANs as energy-based models.
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