Robust control variates for monte carlo integration

Monte Carlo methods are widely used tools employed to estimate functionals of a probability distribution that may be difficult to sample from directly. Given additional information about the distribution or functional of interest, it is often possible to employ variance reduction techniques such as the well-known method of control variates. However, as implemented in practice, this method essentially reduces the empirical sample variance, and is not robust to coefficient estimation error as the number of control variate functions increases. Here we propose two extensions that robustify the control variates method-diagonal and variable loading-and show how to realize them via an iterative implementation that significantly reduces computational cost. These methods are validated using test cases that clearly demonstrate the shortcomings of traditional control variates techniques.