# Automatic LQR Tuning Based on Gaussian Process Global Optimization

arXiv: https://arxiv.org/abs/1605.01950 · HTML: https://mlsanity.com/paper/1605.01950/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2016.

## Built on by (most cited first, 30 of 30)

- [Local policy search with Bayesian optimization](https://mlsanity.com/paper/2106.11899/) (2021)
- [MaxInfoRL: Boosting exploration in reinforcement learning through information gain maximization](https://mlsanity.com/paper/2412.12098/) (2024)
- [GoSafe: Globally Optimal Safe Robot Learning](https://mlsanity.com/paper/2105.13281/) (2021)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Risk-averse Heteroscedastic Bayesian Optimization](https://mlsanity.com/paper/2111.03637/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Benchmarking Potential Based Rewards for Learning Humanoid Locomotion](https://mlsanity.com/paper/2307.10142/) (2023)
- [Meta-Learning Priors for Safe Bayesian Optimization](https://mlsanity.com/paper/2210.00762/) (2022)
- [Optimal Cost Design for Model Predictive Control](https://mlsanity.com/paper/2104.11353/) (2021)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [Safe exploration in reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2503.10352/) (2025)
- [PACSBO: Probably approximately correct safe Bayesian optimization](https://mlsanity.com/paper/2409.01163/) (2024)
- [HYPERmotion: Learning Hybrid Behavior Planning for Autonomous Loco-manipulation](https://mlsanity.com/paper/2406.14655/) (2024)
- [AutoTune: Controller Tuning for High-Speed Flight](https://mlsanity.com/paper/2103.10698/) (2021)
- [Minimisation of Polyak-Lojasewicz Functions Using Random Zeroth-Order Oracles](https://mlsanity.com/paper/2405.09106/) (2024)
- [Simulation-Aided Policy Tuning for Black-Box Robot Learning](https://mlsanity.com/paper/2411.14246/) (2024)
- [The Mini Wheelbot: A Testbed for Learning-based Balancing, Flips, and Articulated Driving](https://mlsanity.com/paper/2502.04582/) (2025)
- [Automated Controller Calibration by Kalman Filtering](https://mlsanity.com/paper/2111.10832/) (2021)
- [Local Bayesian Optimization for Controller Tuning with Crash Constraints](https://mlsanity.com/paper/2411.16267/) (2024)
- [Safety and optimality in learning-based control at low computational cost](https://mlsanity.com/paper/2505.08026/) (2025)
- [Large-Batch, Iteration-Efficient Neural Bayesian Design Optimization](https://mlsanity.com/paper/2306.01095/) (2023)
- [Tracking Control for a Spherical Pendulum via Curriculum Reinforcement Learning](https://mlsanity.com/paper/2309.14096/) (2023)
- [Robust Satisficing Gaussian Process Bandits Under Adversarial Attacks](https://mlsanity.com/paper/2506.01625/) (2025)
- [Efficient Controller Learning from Human Preferences and Numerical Data Via Multi-Modal Surrogate Models](https://mlsanity.com/paper/2603.24138/) (2026)
- [Performance-Driven Controller Tuning via Derivative-Free Reinforcement Learning](https://mlsanity.com/paper/2209.04854/) (2022)
- [Incorporating Recurrent Reinforcement Learning into Model Predictive Control for Adaptive Control in Autonomous Driving](https://mlsanity.com/paper/2301.13313/) (2023)
- [Dependency Structure Search Bayesian Optimization for Decision Making Models](https://mlsanity.com/paper/2308.00629/) (2023)
- [Learning Swing-up Maneuvers for a Suspended Aerial Manipulation Platform in a Hierarchical Control Framework](https://mlsanity.com/paper/2506.13478/) (2025)
- [Towards safe control parameter tuning in distributed multi-agent systems](https://mlsanity.com/paper/2508.13608/) (2025)
- [GUIDE-FBO: Guidance via Uncertainty Intervention and Distributional Exchange for Federated Bayesian Optimization](https://mlsanity.com/paper/2609.35038/) (2026)

## Abstract (arXiv)

This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Results of a two- and four-dimensional tuning problems highlight the method's potential for automatic controller tuning on robotic platforms.