Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Derivative-Free Stochastic Optimization

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Ha, Yunsoo, Mueller, Juliane
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918104454397952
author Ha, Yunsoo
Mueller, Juliane
author_facet Ha, Yunsoo
Mueller, Juliane
contents Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them, and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to the first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic problems and simulation optimization problems involving discrete event systems.
format Preprint
id arxiv_https___arxiv_org_abs_2408_04625
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Derivative-Free Stochastic Optimization
Ha, Yunsoo
Mueller, Juliane
Optimization and Control
Bi-fidelity stochastic optimization has gained increasing attention as an efficient approach to reduce computational costs by leveraging a low-fidelity (LF) model to optimize an expensive high-fidelity (HF) objective. In this paper, we propose ASTRO-BFDF, an adaptive sampling trust region method specifically designed for unconstrained bi-fidelity stochastic derivative-free optimization problems. In ASTRO-BFDF, the LF function serves two purposes: (i) to identify better iterates for the HF function when the optimization process indicates a high correlation between them, and (ii) to reduce the variance of the HF function estimates using bi-fidelity Monte Carlo (BFMC). The algorithm dynamically determines sample sizes while adaptively choosing between crude Monte Carlo and BFMC to balance the trade-off between optimization and sampling errors. We prove that the iterates generated by ASTRO-BFDF converge to the first-order stationary point almost surely. Additionally, we demonstrate the effectiveness of the proposed algorithm through numerical experiments on synthetic problems and simulation optimization problems involving discrete event systems.
title Adaptive Sampling-Based Bi-Fidelity Stochastic Trust Region Method for Derivative-Free Stochastic Optimization
topic Optimization and Control
url https://arxiv.org/abs/2408.04625