{"ID":2831364,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.09055","arxiv_id":"2512.09055","title":"BISTRO -- A Bi-Fidelity Stochastic Gradient Framework using Trust-Regions for Optimization Under Uncertainty","abstract":"Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model to accelerate convergence. Most existing bi-fidelity approaches, however, exploit either design-space curvature or random-space correlation, not both. We present BISTRO - a BI-fidelity Stochastic Trust-Region Optimizer for unconstrained optimization under uncertainty through a stochastic approximation procedure. This approach exploits the curvature information of a low-fidelity objective function to converge within a basin of a local minimum of the high-fidelity model where low-fidelity curvature information is no longer valuable. The method then switches to a variance-reduced stochastic gradient descent procedure. We provide convergence guarantees in expectation under certain regularity assumptions and ensure the best-case $\\mathcal{O}(1/n)$ convergence rate for stochastic optimization. On benchmark problems and a 20-dimensional space shuttle reentry case, BISTRO converges faster than adaptive sampling and variance reduction procedures and cuts computational expense by up to 29x.","short_abstract":"Stochastic optimization of engineering systems is often infeasible due to repeated evaluations of a computationally expensive, high-fidelity simulation. Bi-fidelity methods mitigate this challenge by leveraging a cheaper, approximate model to accelerate convergence. Most existing bi-fidelity approaches, however, exploi...","url_abs":"https://arxiv.org/abs/2512.09055","url_pdf":"https://arxiv.org/pdf/2512.09055v1","authors":"[\"Thomas O. Dixon\",\"Geoffrey F. Bomarito\",\"James E. Warner\",\"Alex A. Gorodetsky\"]","published":"2025-12-09T19:15:35Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"stat.CO\"]","methods":"[]","has_code":false}