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.