# Model-Free Stochastic Reachability Using Kernel Distribution Embeddings

arXiv: https://arxiv.org/abs/1908.00697 · HTML: https://mlsanity.com/paper/1908.00697/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Unifying Goal-Conditioned RL and Unsupervised Skill Learning via Control-Maximization](https://mlsanity.com/paper/2605.06145/) (2026)
- [SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods](https://mlsanity.com/paper/2203.06290/) (2022)
- [Physics-informed Reinforcement Learning for Stochastic Reach-Avoid Analysis](https://mlsanity.com/paper/2608.17117/) (2026)

## Abstract (arXiv)

We present a solution to the terminal-hitting stochastic reach-avoid problem for a Markov control process. This solution takes advantage of a nonparametric representation of the stochastic kernel as a conditional distribution embedding within a reproducing kernel Hilbert space (RKHS). Because the disturbance is modeled as a data-driven stochastic process, this representation avoids intractable integrals in the dynamic recursion of the reach-avoid problem since the expectations can be calculated as an inner product within the RKHS. We demonstrate this approach on a high-dimensional chain of integrators and on Clohessy-Wiltshire-Hill dynamics.