Theoretical guarantees for neural control variates in MCMC
This work provides theoretical guarantees for a variance reduction method in MCMC, which is incremental as it builds on existing control variate techniques with neural networks.
The authors tackled variance reduction in Markov chains using neural network-based control variates, deriving optimal convergence rates for asymptotic variance under different ergodicity assumptions.
In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates are represented as deep neural networks. We derive the optimal convergence rate of the asymptotic variance under various ergodicity assumptions on the underlying Markov chain. The proposed approach relies upon recent results on the stochastic errors of variance reduction algorithms and function approximation theory.