Cross‐Entropy Method

Abstract

The cross‐entropy method is a recent versatile Monte Carlo technique. This article provides a brief introduction to the cross‐entropy method and discusses how it can be used for rare‐event probability estimation and for solving combinatorial, continuous, constrained, and noisy optimization problems. A comprehensive list of references on cross‐entropy methods and applications is included.

A comparison of cross-entropy and variance minimization strategies

“…Although the optimal CE and VM parameter vectors can be obtained analytically for a few specific cases, in general the optimization problems in (2.1) and (2.2) are difficult to solve. Thus, in practice, we often need to estimate v vm or v ce via a multilevel procedure, which we shall call multilevel VM or CE (see [11] for a more thorough discussion).…”

“…In this article we compare two adaptive importance sampling procedures, namely the variance minimization (VM) and cross-entropy (CE) methods [11], [16, pp. 62-83], in the context of rare-event simulation.…”

Monte Carlo Methods for Portfolio Credit Risk

“…In this section we introduce a popular adaptive importance sampling technique for rare-event probability estimation, namely, the Cross Entropy (CE) method. A book-length treatment of the CE method can be found in Rubinstein and Kroese [2004], and a recent review is given in Kroese [2011]. An improved variant that shows better performance in various high-dimensional settings is recently proposed in .…”