  Real world experiments are expensive, and thus it is important to reach a
target in minimum number of experiments. Experimental processes often involve
control variables that changes over time. Such problems can be formulated as a
functional optimisation problem. We develop a novel Bayesian optimisation
framework for such functional optimisation of expensive black-box processes. We
represent the control function using Bernstein polynomial basis and optimise in
the coefficient space. We derive the theory and practice required to
dynamically adjust the order of the polynomial degree, and show how prior
information about shape can be integrated. We demonstrate the effectiveness of
our approach for short polymer fibre design and optimising learning rate
schedules for deep networks.
