  Adaptive Monte Carlo methods are very efficient techniques designed to tune
simulation estimators on-line. In this work, we present an alternative to
stochastic approximation to tune the optimal change of measure in the context
of importance sampling for normal random vectors. Unlike stochastic
approximation, which requires very fine tuning in practice, we propose to use
sample average approximation and deterministic optimization techniques to
devise a robust and fully automatic variance reduction methodology. The same
samples are used in the sample optimization of the importance sampling
parameter and in the Monte Carlo computation of the expectation of interest
with the optimal measure computed in the previous step. We prove that this
highly dependent Monte Carlo estimator is convergent and satisfies a central
limit theorem with the optimal limiting variance. Numerical experiments confirm
the performance of this estimator: in comparison with the crude Monte Carlo
method, the computation time needed to achieve a given precision is divided by
a factor between 3 and 15.
