# On the Design of LQR Kernels for Efficient Controller Learning

arXiv: https://arxiv.org/abs/1709.07089 · HTML: https://mlsanity.com/paper/1709.07089/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2017.

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

- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [Agentic Bayesian Optimization through Surrogate-Augmented Autoresearch](https://mlsanity.com/paper/2608.00316/) (2026)
- [Out of Distribution Detection via Domain-Informed Gaussian Process State Space Models](https://mlsanity.com/paper/2309.06655/) (2023)

## Abstract (arXiv)

Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point and finding the global optimum, BO relies on a probabilistic description of the latent objective function, typically a Gaussian process (GP). As is shown herein, GPs with a common kernel choice can, however, lead to poor learning outcomes on standard quadratic control problems. For a first-order system, we construct two kernels that specifically leverage the structure of the well-known Linear Quadratic Regulator (LQR), yet retain the flexibility of Bayesian nonparametric learning. Simulations of uncertain linear and nonlinear systems demonstrate that the LQR kernels yield superior learning performance.