Importance Sampling using Rényi divergence

We present an alternative approach to the problem of estimating probabilities of rare events and for optimization problems using the class of Rényi divergences of order α > 1. The general procedure we describe does not involve any specific family of distributions, the only restriction is that the search space consists of product form probability density functions. We discuss an algorithm for estimation of probability of rare events and a version for continuous optimization. The results of numerical experimentation with these algorithms carried in the last section support their performances.