# Zero-Order Optimization for Gaussian Process-based Model Predictive Control

arXiv: https://arxiv.org/abs/2211.15522 · HTML: https://mlsanity.com/paper/2211.15522/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 35 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 9 of 9)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [acados: a modular open-source framework for fast embedded optimal control](https://mlsanity.com/paper/1910.13753/) (2019)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Data-Driven MPC for Quadrotors](https://mlsanity.com/paper/2102.05773/) (2021)
- [AMZ Driverless: The Full Autonomous Racing System](https://mlsanity.com/paper/1905.05150/) (2019)
- [HPIPM: a high-performance quadratic programming framework for model predictive control](https://mlsanity.com/paper/2003.02547/) (2020)
- [Cautious NMPC with Gaussian Process Dynamics for Autonomous Miniature Race Cars](https://mlsanity.com/paper/1711.06586/) (2017)

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

- [Learning for CasADi: Data-driven Models in Numerical Optimization](https://mlsanity.com/paper/2312.05873/) (2023)
- [Safe Guaranteed Exploration for Non-linear Systems](https://mlsanity.com/paper/2402.06562/) (2024)
- [Towards safe and tractable Gaussian process-based MPC: Efficient sampling within a sequential quadratic programming framework](https://mlsanity.com/paper/2409.08616/) (2024)
- [A robust and adaptive MPC formulation for Gaussian process models](https://mlsanity.com/paper/2507.02098/) (2025)

## Abstract (arXiv)

By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based control community. Yet, solving the resulting optimal control problem in real-time generally remains a major challenge, due to i) the increased number of augmented states in the optimization problem, as well as ii) computationally expensive evaluations of the posterior mean and covariance and their respective derivatives. To tackle these challenges, we employ i) a tailored Jacobian approximation in a sequential quadratic programming (SQP) approach, and combine it with ii) a parallelizable GP inference and automatic differentiation framework. Reducing the numerical complexity with respect to the state dimension nx for each SQP iteration from O(nx6) to O(nx3), and accelerating GP evaluations on a graphical processing unit, the proposed algorithm computes suboptimal, yet feasible solutions at drastically reduced computation times and exhibits favorable local convergence properties. Numerical experiments verify the scaling properties and investigate the runtime distribution across different parts of the algorithm.