  This paper deals with the speed of convergence of the learning curve in a
Gaussian process regression framework. The learning curve describes the average
generalization error of the Gaussian process used for the regression. More
specifically, it is defined in this paper as the integral of the mean squared
error over the input parameter space with respect to the probability measure of
the input parameters. The main result is the proof of a theorem giving the mean
squared error in function of the number of observations for a large class of
kernels and for any dimension when the number of observations is large. From
this result, we can deduce the asymptotic behavior of the generalization error.
The presented proof generalizes previous ones that were limited to more
specific kernels or to small dimensions (one or two). The result can be used to
build an optimal strategy for resources allocation. This strategy is applied
successfully to a nuclear safety problem.
