NM2-BO: Non-Myopic Multifidelity Bayesian Optimization

Bayesian optimization is a popular framework for the optimization of black box functions. Multifidelity methods allows to accelerate Bayesian optimization by exploiting low-fidelity representations of expensive objective functions. Popular multifidelity Bayesian strategies rely on sampling policies that account for the immediate reward obtained evaluating the objective function at a specific input, precluding greater informative gains that might be obtained looking ahead more steps. This paper proposes a Non-Myopic Multifidelity Bayesian Optimization framework (NM2-BO) to grasp the long-term reward from future steps of the optimization. Our computational strategy comes with a two-step lookahead multifidelity acquisition function that maximizes the cumulative reward obtained measuring the improvement in the solution over two steps ahead. Our NM2-BO algorithm is demonstrated for a large set of benchmark problems to stress test across a broad spectrum of mathematical properties, and a physics-based application relevant for the engineering community. In all the cases, we observe that the proposed algorithm outperforms standard MFBO frameworks.