# Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics

arXiv: https://arxiv.org/abs/1602.04450 · HTML: https://mlsanity.com/paper/1602.04450/

## Key facts

- Cited by 134 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2016.

## Built on by (most cited first, 30 of 134)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2205.11140/) (2022)
- [Joint Entropy Search for Maximally-Informed Bayesian Optimization](https://mlsanity.com/paper/2206.04771/) (2022)
- [Optimal Order Simple Regret for Gaussian Process Bandits](https://mlsanity.com/paper/2108.09262/) (2021)
- [Joint Entropy Search for Multi-objective Bayesian Optimization](https://mlsanity.com/paper/2210.02905/) (2022)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [RoMA: Robust Model Adaptation for Offline Model-based Optimization](https://mlsanity.com/paper/2110.14188/) (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)
- [Transfer Learning for Bayesian Optimization: A Survey](https://mlsanity.com/paper/2302.05927/) (2023)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [ActSafe: Active Exploration with Safety Constraints for Reinforcement Learning](https://mlsanity.com/paper/2410.09486/) (2024)
- [Self-Correcting Bayesian Optimization through Bayesian Active Learning](https://mlsanity.com/paper/2304.11005/) (2023)
- [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)
- [Active Learning and Bayesian Optimization: a Unified Perspective to Learn with a Goal](https://mlsanity.com/paper/2303.01560/) (2023)
- [Safe Learning and Optimization Techniques: Towards a Survey of the State of the Art](https://mlsanity.com/paper/2101.09505/) (2021)
- [Bayesian optimization as a flexible and efficient design framework for sustainable process systems](https://mlsanity.com/paper/2401.16373/) (2024)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Safe Reinforcement Learning on the Constraint Manifold: Theory and Applications](https://mlsanity.com/paper/2404.09080/) (2024)
- [Improved Regret Analysis in Gaussian Process Bandits: Optimality for Noiseless Reward, RKHS norm, and Non-Stationary Variance](https://mlsanity.com/paper/2502.06363/) (2025)
- [Meta-Learning Priors for Safe Bayesian Optimization](https://mlsanity.com/paper/2210.00762/) (2022)
- [Safe Active Learning for Multi-Output Gaussian Processes](https://mlsanity.com/paper/2203.14849/) (2022)
- [Distributed Contextual Linear Bandits with Minimax Optimal Communication Cost](https://mlsanity.com/paper/2205.13170/) (2022)
- [On Controller Tuning with Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2207.11120/) (2022)
- [UCB-based Algorithms for Multinomial Logistic Regression Bandits](https://mlsanity.com/paper/2103.11489/) (2021)
- [Computationally Efficient High-Dimensional Bayesian Optimization via Variable Selection](https://mlsanity.com/paper/2109.09264/) (2021)
- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning](https://mlsanity.com/paper/2207.10415/) (2022)

## Abstract (arXiv)

Robotic algorithms typically depend on various parameters, the choice of which significantly affects the robot's performance. While an initial guess for the parameters may be obtained from dynamic models of the robot, parameters are usually tuned manually on the real system to achieve the best performance. Optimization algorithms, such as Bayesian optimization, have been used to automate this process. However, these methods may evaluate unsafe parameters during the optimization process that lead to safety-critical system failures. Recently, a safe Bayesian optimization algorithm, called SafeOpt, has been developed, which guarantees that the performance of the system never falls below a critical value; that is, safety is defined based on the performance function. However, coupling performance and safety is often not desirable in robotics. For example, high-gain controllers might achieve low average tracking error (performance), but can overshoot and violate input constraints. In this paper, we present a generalized algorithm that allows for multiple safety constraints separate from the objective. Given an initial set of safe parameters, the algorithm maximizes performance but only evaluates parameters that satisfy safety for all constraints with high probability. To this end, it carefully explores the parameter space by exploiting regularity assumptions in terms of a Gaussian process prior. Moreover, we show how context variables can be used to safely transfer knowledge to new situations and tasks. We provide a theoretical analysis and demonstrate that the proposed algorithm enables fast, automatic, and safe optimization of tuning parameters in experiments on a quadrotor vehicle.