Gaussian process optimization through sampling from the maximum distribution

This paper first presents a novel algorithm approximating the distribution of the maximum (both its position and its value) of a Gaussian process. This algorithm uses particles in a similar way as Sequential Monte Carlo samplers. It is subsequently applied to the problem of Gaussian Process Optimization (GPO). The resulting GPO algorithm does not use an acquisition function, which makes it different from other GPO algorithms. Through various example problems, including a wind turbine load mitigation example, we find that the resulting algorithm on average outperforms existing GPO algorithms. In addition, because no acquisition function has to be optimized, the algorithm can easily and efficiently be applied to problems with high-dimensional input spaces.