Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation

• 成果类型: Article
• 署名作者: He, Shengyi; Jiang, Guangxin; Lam, Henry; Fu, Michael C.
• 署名单位: Columbia University; Harbin Institute of Technology; University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.2484
• 发表日期: 2024
• 页码: 2612-2630
• 关键词: rare-event simulation; Large deviations theory; excessive backlogs; approximation; systems

摘要

In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance sampling can be employed to drive down the sampling error to a desirable level. However, selecting a good importance sampler requires knowledge of the solution to the problem at hand, which is the goal to begin with and thus forms a circular challenge. We investigate the use of adaptive importance sampling to untie this circularity. Our procedure sequentially updates the importance sampler to reach the optimal sampler and the optimal solution simultaneously, and can be embedded in both sample-average-approximation-type algorithms and stochastic-approximation-type algorithms. Our theoretical analysis establishes strong consistency and asymptotic normality of the resulting estimators. We also demonstrate, via a minimax perspective, the key role of using adaptivity in controlling asymptotic errors. Finally, we illustrate the effectiveness of our approach via numerical experiments.