# Adaptive Importance Sampling for Efficient Stochastic Root Finding and Quantile Estimation

arXiv: https://arxiv.org/abs/2102.10631 · HTML: https://mlsanity.com/paper/2102.10631/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2021.

## Built on by (most cited first, 3 of 3)

- [Stochastic Optimization with Optimal Importance Sampling](https://mlsanity.com/paper/2504.03560/) (2025)
- [Pure Exploration via Frank-Wolfe Self-Play](https://mlsanity.com/paper/2509.19901/) (2025)
- [Optimal low-rank stochastic gradient estimation for LLM training](https://mlsanity.com/paper/2603.20632/) (2026)

## Abstract (arXiv)

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 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.