Scalable Control Variates for Monte Carlo Methods via Stochastic Optimization
This work addresses scalability issues in Monte Carlo estimation for high-dimensional and large-sample problems, though it is incremental as it builds on existing Stein operator approaches.
The paper tackled the computational cost of control variates in large-scale Monte Carlo methods by proposing a scalable framework using Stein operators and stochastic optimization, achieving effective variance reduction as demonstrated in Bayesian inference applications.
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 a substantial computational cost. This paper considers control variates based on Stein operators, presenting a framework that encompasses and generalizes existing approaches that use polynomials, kernels and neural networks. A learning strategy based on minimising a variational objective through stochastic optimization is proposed, leading to scalable and effective control variates. Novel theoretical results are presented to provide insight into the variance reduction that can be achieved, and an empirical assessment, including applications to Bayesian inference, is provided in support.