  Multi-fidelity Bayesian Optimisation (MFBO) has been shown to generally
converge faster than single-fidelity Bayesian Optimisation (SFBO) (Poloczek et
al. (2017)). Inspired by recent benchmark papers, we are investigating the
long-run behaviour of MFBO, based on observations in the literature that it
might under-perform in certain scenarios (Mikkola et al. (2023), Eggensperger
et al. (2021)). An under-performance of MBFO in the long-run could
significantly undermine its application to many research tasks, especially when
we are not able to identify when the under-performance begins. We create a
simple benchmark study, showcase empirical results and discuss scenarios and
possible reasons of under-performance.
