2022/06/15 by Anthony Gruber, Gruber, Anthony, Max Gunzburger +5
Computer Science · Decision Sciences · Engineering · Mathematics · #49M20 #62K05 #Advanced Multi-Objective Optimization Algorithms #Algorithm #Computer science #Engineering #Estimation #FOS: Mathematics #Hybrid Monte Carlo #Manufacturing Process and Optimization #Markov chain Monte Carlo #Mathematical optimization #Mathematics #Monte Carlo integration #Monte Carlo method #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Probabilistic and Robust Engineering Design #Reduction (mathematics) #Simple (philosophy) #Statistics #Usability #Variance (accounting) #Variance reduction
paper · pdf · doi:10.48550/arxiv.2206.07572
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.