Cost-Aware Bayesian Optimization With Automatic Stop Condition Under Multi-Fidelity Constraints and Data

Abstract Bayesian optimization (BO) is increasingly employed in critical applications such as materials design to find optimal solutions with minimal costs. While BO is known for its sample efficiency, relying solely on costly high-fidelity data can still result in high overall costs, especially in constrained search spaces where both optimization and feasibility must be ensured. A related issue in the BO literature is the lack of a systematic stopping criterion, which causes most methods to simply rely on the maximum number of iterations or improvement threshold. This issue affects single-fidelity and multifidelity problems with or without constraints, reducing the sample efficiency of BO. To solve these challenges, we develop a constrained cost-aware multifidelity BO (CMFBO) framework whose goal is to minimize overall sampling costs by utilizing inexpensive low-fidelity sources while ensuring feasibility and handling source-dependent noise. Our approach accommodates constraints that vary across data sources and may be even black-box functions. We also introduce a systematic stopping criterion to resolve the long-lasting issue associated with BO’s convergence assessment. Our framework is publicly available on GitHub through the gp+ python package, and herein, we validate its efficacy on multiple benchmark problems.