  This works extends the Random Embedding Bayesian Optimization approach by
integrating a warping of the high dimensional subspace within the covariance
kernel. The proposed warping, that relies on elementary geometric
considerations, allows mitigating the drawbacks of the high extrinsic
dimensionality while avoiding the algorithm to evaluate points giving redundant
information. It also alleviates constraints on bound selection for the embedded
domain, thus improving the robustness, as illustrated with a test case with 25
variables and intrinsic dimension 6.
