Variance Reduction

Variance reduction studies how to make noisy estimates—such as gradients, Monte Carlo expectations, policy values, and experiment effects—more precise without simply collecting more samples. Common approaches include control variates, recursive estimators such as SVRG and STORM, importance and stratified sampling, and Rao-Blackwellization or shared randomness. The methods are studied in finite-sum optimization and sampling as well as reinforcement learning, diffusion-model training, Bayesian computation, and A/B testing, with evaluations often measuring variance, sample complexity, or convergence. A central tension is that lower estimator variance may require extra computation or stronger assumptions, and minimizing variance alone does not always improve downstream outcomes such as model quality.