# Stochastic Optimal Control via Hilbert Space Embeddings of Distributions

arXiv: https://arxiv.org/abs/2103.12759 · HTML: https://mlsanity.com/paper/2103.12759/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2021.

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

- [SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods](https://mlsanity.com/paper/2203.06290/) (2022)
- [Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control](https://mlsanity.com/paper/2301.03565/) (2023)
- [Kernel-Based Safe Exploration in Deep Reinforcement Learning](https://mlsanity.com/paper/2605.22207/) (2026)

## Abstract (arXiv)

Kernel embeddings of distributions have recently gained significant attention in the machine learning community as a data-driven technique for representing probability distributions. Broadly, these techniques enable efficient computation of expectations by representing integral operators as elements in a reproducing kernel Hilbert space. We apply these techniques to the area of stochastic optimal control theory and present a method to compute approximately optimal policies for stochastic systems with arbitrary disturbances. Our approach reduces the optimization problem to a linear program, which can easily be solved via the Lagrangian dual, without resorting to gradient-based optimization algorithms. We focus on discrete-time dynamic programming, and demonstrate our proposed approach on a linear regulation problem, and on a nonlinear target tracking problem. This approach is broadly applicable to a wide variety of optimal control problems, and provides a means of working with stochastic systems in a data-driven setting.