Langevin Quasi-Monte Carlo

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density \pi(\theta)\propto \exp(-U(\theta)), LMC iteratively generates the next sample by taking a step in the gradient direction abla U with added Gaussian perturbations. Expectations w.r.t. the target distribution \pi are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples.