# Stochastic Control with Signatures

arXiv: https://arxiv.org/abs/2406.01585 · HTML: https://mlsanity.com/paper/2406.01585/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2024.

## Built on by (most cited first, 6 of 6)

- [The Volterra signature](https://mlsanity.com/paper/2603.04525/) (2026)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)
- [Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version](https://mlsanity.com/paper/2604.13147/) (2026)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)
- [The Linear Representation Hypothesis for Vision-Language-Action Models](https://mlsanity.com/paper/2609.30996/) (2026)

## Abstract (arXiv)

This paper proposes to parameterize open loop controls in stochastic optimal control problems via suitable classes of functionals depending on the driver's path signature, a concept adopted from rough path integration theory. We rigorously prove that these controls are dense in the class of progressively measurable controls and use rough path methods to establish suitable conditions for stability of the controlled dynamics and target functional. These results pave the way for Monte Carlo methods to stochastic optimal control for generic target functionals and dynamics. We discuss the rather versatile numerical algorithms for computing approximately optimal controls and verify their accurateness in benchmark problems from Mathematical Finance.