# Variational approach to rare event simulation using least-squares regression

arXiv: https://arxiv.org/abs/1901.09195 · HTML: https://mlsanity.com/paper/1901.09195/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2019.

## Built on by (most cited first, 12 of 12)

- [Stochastic Optimal Control Matching](https://mlsanity.com/paper/2312.02027/) (2023)
- [Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference](https://mlsanity.com/paper/2508.12511/) (2025)
- [Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems](https://mlsanity.com/paper/2112.03749/) (2021)
- [Solving high-dimensional parabolic PDEs using the tensor train format](https://mlsanity.com/paper/2102.11830/) (2021)
- [Stochastic Optimal Control for Diffusion Bridges in Function Spaces](https://mlsanity.com/paper/2405.20630/) (2024)
- [Robust SDE-Based Variational Formulations for Solving Linear PDEs via Deep Learning](https://mlsanity.com/paper/2206.10588/) (2022)
- [A Taxonomy of Loss Functions for Stochastic Optimal Control](https://mlsanity.com/paper/2410.00345/) (2024)
- [From continuous-time formulations to discretization schemes: tensor trains and robust regression for BSDEs and parabolic PDEs](https://mlsanity.com/paper/2307.15496/) (2023)
- [Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions](https://mlsanity.com/paper/2206.03369/) (2022)
- [Estimating Committor Functions via Deep Adaptive Sampling on Rare Transition Paths](https://mlsanity.com/paper/2501.15522/) (2025)
- [End-To-End Learning of Gaussian Mixture Priors for Diffusion Sampler](https://mlsanity.com/paper/2503.00524/) (2025)
- [Machine learning kinetics from molecular dynamics data](https://mlsanity.com/paper/2609.17736/) (2026)

## Abstract (arXiv)

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e. zero-variance) change of measure and exploits the fact that the latter can be rephrased as a stochastic optimal control problem. The control problem can be solved by a stochastic approximation algorithm, using the Feynman-Kac representation of the associated dynamic programming equations, and we discuss numerical aspects for high-dimensional problems along with simple toy examples.