  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.
