Scalable Control Variates for Monte Carlo Methods Via Stochastic Optimization

Control variates are a well-established tool to reduce the variance of Monte Carlo estimators. However, for large-scale problems including high-dimensional and large-sample settings, their advantages can be outweighed by substantial computational cost. This paper considers control based on Stein operators, presenting framework that encompasses generalizes existing approaches use polynomials, kernels neural networks. A learning strategy minimizing variational objective through stochastic optimization is proposed, leading scalable effective variates. Novel theoretical results presented provide insight into reduction achieved, an empirical assessment, applications Bayesian inference, provided in support.