This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: firstly, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical Expected Improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Secondly, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety.
