  We consider the problem of adaptive stratified sampling for Monte Carlo
integration of a differentiable function given a finite number of evaluations
to the function. We construct a sampling scheme that samples more often in
regions where the function oscillates more, while allocating the samples such
that they are well spread on the domain (this notion shares similitude with low
discrepancy). We prove that the estimate returned by the algorithm is almost
similarly accurate as the estimate that an optimal oracle strategy (that would
know the variations of the function everywhere) would return, and provide a
finite-sample analysis.
