2021/10/29 by Anna Korba, Korba, Anna, François Portier +1 · 1 citation
Decision Sciences · Engineering · Mathematics · #62L20 #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Mathematical Approximation and Integration #Nuclear reactor physics and engineering #Probabilistic and Robust Engineering Design #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2110.15590
openalex publication_date 2021/10/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Adaptive importance sampling is a widely spread Monte Carlo technique that\nuses a re-weighting strategy to iteratively estimate the so-called target\ndistribution. A major drawback of adaptive importance sampling is the large\nvariance of the weights which is known to badly impact the accuracy of the\nestimates. This paper investigates a regularization strategy whose basic\nprinciple is to raise the importance weights at a certain power. This\nregularization parameter, that might evolve between zero and one during the\nalgorithm, is shown (i) to balance between the bias and the variance and (ii)\nto be connected to the mirror descent framework. Using a kernel density\nestimate to build the sampling policy, the uniform convergence is established\nunder mild conditions. Finally, several practical ways to choose the\nregularization parameter are discussed and the benefits of the proposed\napproach are illustrated empirically.\n