On the development of a practical Bayesian optimisation algorithm for
  expensive experiments and simulations with changing environmental conditions
Mike Diessner Kevin J. Wilson Richard D. Whalley
Experiments in engineering are typically conducted in controlled environments
where parameters can be set to any desired value. This assumes that the same
applies in a real-world setting -- an assumption that is often incorrect as
many experiments are influenced by uncontrollable environmental conditions such
as temperature, humidity and wind speed. When optimising such experiments, the
focus should lie on finding optimal values conditionally on these
uncontrollable variables. This article extends Bayesian optimisation to the
optimisation of systems in changing environments that include controllable and
uncontrollable parameters. The extension fits a global surrogate model over all
controllable and environmental variables but optimises only the controllable
parameters conditional on measurements of the uncontrollable variables. The
method is validated on two synthetic test functions and the effects of the
noise level, the number of the environmental parameters, the parameter
fluctuation, the variability of the uncontrollable parameters, and the
effective domain size are investigated. ENVBO, the proposed algorithm resulting
from this investigation, is applied to a wind farm simulator with eight
controllable and one environmental parameter. ENVBO finds solutions for the
full domain of the environmental variable that outperforms results from
optimisation algorithms that only focus on a fixed environmental value in all
but one case while using a fraction of their evaluation budget. This makes the
proposed approach very sample-efficient and cost-effective. An off-the-shelf
open-source version of ENVBO is available via the NUBO Python package.