Sequential design for prediction Sequential design for prediction with Gaussian process models

When numerical simulations are time consuming, the simulator is replaced by a simple (meta-)model which approximates its behavior. This surrogate model is adjusted on a set of carefully chosen computer experiments, or Design of Experiments (DoE), with the objective of obtaining the best possible approximation with available computational budget. For the widely used Gaussian process models, Mutual Information (MI) is a particularly attractive DoE quality measure. Finding the set of configurations that optimise the MI criterion is a NP-hard problem, and in this paper we concentrate on the sequential construction of designs by greedily maximising MI. Unfortunately, even this much simpler problem is still computationally demanding, still involving prohibitively large running times. We propose a new algorithm for the sequential construction of MI-optimal designs that shares computational costs across several candidate points, enabling a significant reduction of computing time. In particular, we show that the combination of our approach with a Lazy-greedy strategy proposed previously leads to important computational gains, enabling the consideration of more challenging problems (higher dimensional problems, finer grids of design points). A comprehensive numerical study highlights the increased invariance of the computational costs of the new algorithm with respect to implementation choices, like the covariance kernel