# SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods

arXiv: https://arxiv.org/abs/2203.06290 · HTML: https://mlsanity.com/paper/2203.06290/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 55 references that are in the map.
- First posted on arXiv 12 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Measure-Theoretic Approach to Kernel Conditional Mean Embeddings](https://mlsanity.com/paper/2002.03689/) (2020)
- [Learning Human Objectives by Evaluating Hypothetical Behavior](https://mlsanity.com/paper/1912.05652/) (2019)
- [Learning Model Predictive Control for iterative tasks. A Data-Driven Control Framework](https://mlsanity.com/paper/1609.01387/) (2016)
- [A storm is Coming: A Modern Probabilistic Model Checker](https://mlsanity.com/paper/1702.04311/) (2017)
- [FAUST2: Formal Abstractions of Uncountable-STate STochastic processes](https://mlsanity.com/paper/1403.3286/) (2014)
- [ProbReach: Verified Probabilistic Delta-Reachability for Stochastic Hybrid Systems](https://mlsanity.com/paper/1410.8060/) (2014)
- [Functional Gradient Motion Planning in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/1601.03648/) (2016)
- [Model-Free Stochastic Reachability Using Kernel Distribution Embeddings](https://mlsanity.com/paper/1908.00697/) (2019)
- [Learning Approximate Forward Reachable Sets Using Separating Kernels](https://mlsanity.com/paper/2011.09678/) (2020)
- [Stochastic Optimal Control via Hilbert Space Embeddings of Distributions](https://mlsanity.com/paper/2103.12759/) (2021)
- [SReachTools Kernel Module: Data-Driven Stochastic Reachability Using Hilbert Space Embeddings of Distributions](https://mlsanity.com/paper/2011.10610/) (2020)

## Built on by (most cited first, 1 of 1)

- [Safety Certification is Classification](https://mlsanity.com/paper/2605.06087/) (2026)

## Abstract (arXiv)

We present SOCKS, a data-driven stochastic optimal control toolbox based in kernel methods. SOCKS is a collection of data-driven algorithms that compute approximate solutions to stochastic optimal control problems with arbitrary cost and constraint functions, including stochastic reachability, which seeks to determine the likelihood that a system will reach a desired target set while respecting a set of pre-defined safety constraints. Our approach relies upon a class of machine learning algorithms based in kernel methods, a nonparametric technique which can be used to represent probability distributions in a high-dimensional space of functions known as a reproducing kernel Hilbert space. As a nonparametric technique, kernel methods are inherently data-driven, meaning that they do not place prior assumptions on the system dynamics or the structure of the uncertainty. This makes the toolbox amenable to a wide variety of systems, including those with nonlinear dynamics, black-box elements, and poorly characterized stochastic disturbances. We present the main features of SOCKS and demonstrate its capabilities on several benchmarks.