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.

翻译：适应性重要性抽样是一种广泛推广的蒙特卡洛技术,它使用重新加权战略迭接估计所谓的目标分布;适应性重要性抽样的一个主要缺点是已知对估计准确性有严重影响的重量差异很大;本文调查了一种正规化战略,其基本原则是提高某一力量的重量;这一正规化参数在算法期间可能在零和1之间演化,显示(一) 平衡偏差和差异;(二) 与镜像下沉框架连接;利用内核密度估计来建立抽样政策,统一趋同是在温和的条件下建立的;最后,讨论了选择正规化参数的若干实际方法,并用经验说明拟议方法的好处。