A Comparison of Cross-entropy and Variance Min- Imization Strategies

The variance minimization (VM) and cross-entropy (CE) methods are two versatile adaptive importance sampling procedures that have been successfully applied to a wide variety of difficult rare-event estimation problems. We compare these two methods via various examples where the optimal VM and CE importance densities can be obtained analytically. We find that in the cases studied both VM and CE methods prescribe the same importance sampling parameters, suggesting that the criterion of minimizing the crossentropy distance might be asymptotically identical to minimizing the variance of the associated importance sampling estimator.