Non-Myopic Multifidelity Bayesian Optimization
Francesco Di Fiore, Laura Mainini
TL;DR
This work tackles expensive black‑box optimization by marrying multifidelity Gaussian process surrogates with a non‑myopic, two‑step lookahead acquisition. It frames MFBO as a dynamic programming problem and derives a two‑step lookahead acquisition function $U^{\pi^{*}}_z = MFEI(\mathbf{x}_{z+1}, l_{z+1}) + \mathbb{E}[\max(MFEI(\mathbf{x}_{z+2}, l_{z+2}))]$, approximating the nested expectations via Monte Carlo to enable scalable optimization. The approach is evaluated on benchmarks including Forrester, Rosenbrock, Rastrigin, Mass‑Spring, and Borehole, consistently outperforming standard MFBO in terms of faster convergence under a given budget, while accommodating any finite number of fidelities. The method offers a practical tool for engineering and scientific optimization where expensive evaluations and multiple fidelity sources are available, enabling more efficient discovery of high‑quality solutions.
Abstract
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 framework 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. We demonstrate that the proposed algorithm outperforms a standard multifidelity Bayesian framework on popular benchmark optimization problems.