  Scientific experiments are usually expensive due to complex experimental
preparation and processing. Experimental design is therefore involved with the
task of finding the optimal experimental input that results in the desirable
output by using as few experiments as possible. Experimenters can often acquire
the knowledge about the location of the global optimum. However, they do not
know how to exploit this knowledge to accelerate experimental design. In this
paper, we adopt the technique of Bayesian optimization for experimental design
since Bayesian optimization has established itself as an efficient tool for
optimizing expensive black-box functions. Again, it is unknown how to
incorporate the expert prior knowledge about the global optimum into Bayesian
optimization process. To address it, we represent the expert knowledge about
the global optimum via placing a prior distribution on it and we then derive
its posterior distribution. An efficient Bayesian optimization approach has
been proposed via posterior sampling on the posterior distribution of the
global optimum. We theoretically analyze the convergence of the proposed
algorithm and discuss the robustness of incorporating expert prior. We evaluate
the efficiency of our algorithm by optimizing synthetic functions and tuning
hyperparameters of classifiers along with a real-world experiment on the
synthesis of short polymer fiber. The results clearly demonstrate the
advantages of our proposed method.
