  Bayesian Optimization using Gaussian Processes is a popular approach to deal
with the optimization of expensive black-box functions. However, because of the
a priori on the stationarity of the covariance matrix of classic Gaussian
Processes, this method may not be adapted for non-stationary functions involved
in the optimization problem. To overcome this issue, a new Bayesian
Optimization approach is proposed. It is based on Deep Gaussian Processes as
surrogate models instead of classic Gaussian Processes. This modeling technique
increases the power of representation to capture the non-stationarity by simply
considering a functional composition of stationary Gaussian Processes,
providing a multiple layer structure. This paper proposes a new algorithm for
Global Optimization by coupling Deep Gaussian Processes and Bayesian
Optimization. The specificities of this optimization method are discussed and
highlighted with academic test cases. The performance of the proposed algorithm
is assessed on analytical test cases and an aerospace design optimization
problem and compared to the state-of-the-art stationary and non-stationary
Bayesian Optimization approaches.
