Variance reduction for MCMC methods via martingale representations

In this paper we propose an efficient variance reduction approach for MCMC algorithms relying on a novel discrete time martingale representation for Markov chains. Our approach is fully non-asymptotic and does not require any type of ergodicity or special product structure of the underlying density. By rigorously analyzing the convergence of the proposed algorithm, we show that it's complexity is indeed significantly smaller than one of the original MCMC algorithm. The numerical performance of the new method is illustrated in the case of Gaussian mixtures and binary regression.