Bias-Variance Techniques for Monte Carlo Optimization: Cross-validation for the CE Method

TL;DR

This paper explores how bias-variance tradeoff and cross-validation can be used to improve the performance of Monte Carlo Optimization algorithms, specifically the Cross Entropy method, by leveraging techniques from Parametric Learning.

Contribution

It demonstrates the application of cross-validation, a bias-variance based technique, to enhance the effectiveness of the CE method in Monte Carlo Optimization.

Findings

Cross-validation significantly improves CE method performance.

Bias-variance tradeoff is crucial for optimizing MCO algorithms.

PL techniques can be adapted to enhance MCO algorithms.

Abstract

In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL algorithms is the bias-variance tradeoff. This tradeoff has been used to improve PL algorithms ranging from Monte Carlo estimation of integrals, to linear estimation, to general statistical estimation. Moreover, as described by, MCO is very closely related to PL. Owing to this similarity, the bias-variance tradeoff affects MCO performance, just as it does PL performance. In this article, we exploit the bias-variance tradeoff to enhance the performance of MCO algorithms. We use the technique of cross-validation, a technique based on the bias-variance tradeoff, to significantly improve the performance of the Cross Entropy (CE) method, which is an MCO algorithm. In previous work we have confirmed that other PL techniques improve the perfomance of other MCO algorithms. We conclude that the many techniques pioneered in PL could be investigated as ways to improve MCO algorithms in general, and the CE method in particular.