# Gaussian Processes with State-Dependent Noise for Stochastic Control

arXiv: https://arxiv.org/abs/2305.16229 · HTML: https://mlsanity.com/paper/2305.16229/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 8 of 8)

- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [A Survey of Constrained Gaussian Process Regression: Approaches and Implementation Challenges](https://mlsanity.com/paper/2006.09319/) (2020)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)
- [Gaussian Process based Stochastic Model Predictive Control for Cooperative Adaptive Cruise Control](https://mlsanity.com/paper/2111.07162/) (2021)
- [Constrained Gaussian Process Learning for Model Predictive Control](https://mlsanity.com/paper/1911.10809/) (2019)

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

- [Theoretical Analysis of Heteroscedastic Gaussian Processes with Posterior Distributions](https://mlsanity.com/paper/2409.12622/) (2024)

## Abstract (arXiv)

This paper considers a stochastic control framework, in which the residual model uncertainty of the dynamical system is learned using a Gaussian Process (GP). In the proposed formulation, the residual model uncertainty consists of a nonlinear function and state-dependent noise. The proposed formulation uses a posterior-GP to approximate the residual model uncertainty and a prior-GP to account for state-dependent noise. The two GPs are interdependent and are thus learned jointly using an iterative algorithm. Theoretical properties of the iterative algorithm are established. Advantages of the proposed state-dependent formulation include (i) faster convergence of the GP estimate to the unknown function as the GP learns which data samples are more trustworthy and (ii) an accurate estimate of state-dependent noise, which can, e.g., be useful for a controller or decision-maker to determine the uncertainty of an action. Simulation studies highlight these two advantages.