In multiple importance sampling we combine samples from a finite list of proposal distributions. When those proposal distributions are used to create control variates, it is possible (Owen and Zhou, 2000) to bound the ratio of the resulting variance to that of the unknown best proposal distribution in our list. The minimax regret arises by taking a uniform mixture of proposals, but that is conservative when there are many components. In this paper we optimize the mixture component sampling rates to gain further efficiency. We show that the sampling variance of mixture importance sampling with control variates is jointly convex in the mixture probabilities and control variate regression coefficients. We also give a sequential importance sampling algorithm to estimate the optimal mixture from the sample data.
Meanwhile, REF bound the regret for multiple importance sampling where the proposal distribution is a mixture of a finite number of proposal distributions, by bounding the variance of the importance sampling estimates with the help of control variates.
Optimal mixture weights in multiple importance sampling
arXiv: Computation
Mathematics