Robust tuning of Robbins-Monro algorithm for quantile estimation in iterative uncertainty quantification

In uncertainty quantification of a numerical simulation model output, the classical approach for quantile estimation requires the availability of the full sample of the studied variable. This approach is not suitable at exascale as large ensembles of simulation runs would need to gather a prohibitively large amount of data. This problem can be solved thanks to an on-the-fly (iterative) approach based on the Robbins-Monro algorithm. We numerically study this algorithm for estimating a discretized quantile function from samples of limited size (a few hundreds observations). As in practice, the distribution of the underlying variable is unknown, the goal is to define "robust" values of the algorithm parameters, which means that quantile estimates have to be reasonably good in most situations. This paper present new empirically-validated iterative quantile estimators, for two different practical situations: when the final number of the model runs N is a priori fixed and when N is unknown in advance (it can then be minimized during the study in order to save cpu time cost)