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This paper deals with the speed of convergence of the learning curve in aGaussian process regression framework. The learning curve describes the averagegeneralization error of the Gaussian process used for the regression. Morespecifically, it is defined in this paper as the integral of the mean squarederror over the input parameter space with respect to the probability measure ofthe input parameters. The main result is the proof of a theorem giving the meansquared error in function of the number of observations for a large class ofkernels and for any dimension when the number of observations is large. Fromthis result, we can deduce the asymptotic behavior of the generalization error.The presented proof generalizes previous ones that were limited to morespecific kernels or to small dimensions (one or two). The result can be used tobuild an optimal strategy for resources allocation. This strategy is appliedsuccessfully to a nuclear safety problem.

Regularity dependence of the rate of convergence of the learning curve for Gaussian process regression