Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track
Sergey Samsonov, Evgeny Lagutin, Marylou Gabrié, Alain Durmus, Alexey Naumov, Eric Moulines
Recent works leveraging learning to enhance sampling have shown promising results, in particular by designing effective non-local moves and global proposals. However, learning accuracy is inevitably limited in regions where little data is available such as in the tails of distributions as well as in high-dimensional problems. In the present paper we study an Explore-Exploit Markov chain Monte Carlo strategy ($\operatorname{Ex^2MCMC}$) that combines local and global samplers showing that it enjoys the advantages of both approaches. We prove $V$-uniform geometric ergodicity of $\operatorname{Ex^2MCMC}$ without requiring a uniform adaptation of the global sampler to the target distribution. We also compute explicit bounds on the mixing rate of the Explore-Exploit strategy under realistic conditions. Moreover, we propose an adaptive version of the strategy ($\operatorname{FlEx^2MCMC}$) where a normalizing flow is trained while sampling to serve as a proposal for global moves. We illustrate the efficiency of $\operatorname{Ex^2MCMC}$ and its adaptive version on classical sampling benchmarks as well as in sampling high-dimensional distributions defined by Generative Adversarial Networks seen as Energy Based Models.