  Adaptive importance sampling is a widely spread Monte Carlo technique that
uses a re-weighting strategy to iteratively estimate the so-called target
distribution. A major drawback of adaptive importance sampling is the large
variance of the weights which is known to badly impact the accuracy of the
estimates. This paper investigates a regularization strategy whose basic
principle is to raise the importance weights at a certain power. This
regularization parameter, that might evolve between zero and one during the
algorithm, is shown (i) to balance between the bias and the variance and (ii)
to be connected to the mirror descent framework. Using a kernel density
estimate to build the sampling policy, the uniform convergence is established
under mild conditions. Finally, several practical ways to choose the
regularization parameter are discussed and the benefits of the proposed
approach are illustrated empirically.
