A Multifidelity Monte Carlo Method for Realistic Computational Budgets

TL;DR

This paper introduces a flexible multifidelity Monte Carlo method that optimizes statistical estimation within any computational budget, improving variance reduction over traditional Monte Carlo methods.

Contribution

It extends existing MFMC algorithms with a sequence of closed-form optimization solutions, making it applicable to any computational budget and maintaining optimality.

Findings

Achieves at least as good variance reduction as existing MFMC methods.

Works effectively across a wide range of computational budgets.

Provides theoretical guarantees of optimality.

Abstract

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing closed-form solution, this method extends the usability of a well known MFMC algorithm, recovering it when the computational budget is large enough. Theoretical results verify that the proposed approach is at least as optimal as its namesake and retains the benefits of multifidelity estimation with minimal assumptions on the budget or amount of available data, providing a notable reduction in variance over simple Monte Carlo estimation.