# GoSafe: Globally Optimal Safe Robot Learning

arXiv: https://arxiv.org/abs/2105.13281 · HTML: https://mlsanity.com/paper/2105.13281/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 27 May 2021.

## Builds on (most cited first, 17 of 17)

- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [On Kernelized Multi-armed Bandits](https://mlsanity.com/paper/1704.00445/) (2017)
- [A Lyapunov-based Approach to Safe Reinforcement Learning](https://mlsanity.com/paper/1805.07708/) (2018)
- [Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics](https://mlsanity.com/paper/1602.04450/) (2016)
- [Bayesian Optimization with Unknown Constraints](https://mlsanity.com/paper/1403.5607/) (2014)
- [Safe Controller Optimization for Quadrotors with Gaussian Processes](https://mlsanity.com/paper/1509.01066/) (2015)
- [Safe Exploration in Finite Markov Decision Processes with Gaussian Processes](https://mlsanity.com/paper/1606.04753/) (2016)
- [Safe Exploration for Interactive Machine Learning](https://mlsanity.com/paper/1910.13726/) (2019)
- [A General Framework for Constrained Bayesian Optimization using Information-based Search](https://mlsanity.com/paper/1511.09422/) (2015)
- [Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes](https://mlsanity.com/paper/1603.04915/) (2016)
- [Automatic LQR Tuning Based on Gaussian Process Global Optimization](https://mlsanity.com/paper/1605.01950/) (2016)
- [Robust Model-free Reinforcement Learning with Multi-objective Bayesian Optimization](https://mlsanity.com/paper/1910.13399/) (2019)
- [Robot Learning with Crash Constraints](https://mlsanity.com/paper/2010.08669/) (2020)
- [Deep Kernels for Optimizing Locomotion Controllers](https://mlsanity.com/paper/1707.09062/) (2017)
- [A Learnable Safety Measure](https://mlsanity.com/paper/1910.02835/) (2019)
- [Excursion Search for Constrained Bayesian Optimization under a Limited Budget of Failures](https://mlsanity.com/paper/2005.07443/) (2020)

## Built on by (most cited first, 27 of 27)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [ActSafe: Active Exploration with Safety Constraints for Reinforcement Learning](https://mlsanity.com/paper/2410.09486/) (2024)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [A Human-Centered Safe Robot Reinforcement Learning Framework with Interactive Behaviors](https://mlsanity.com/paper/2302.13137/) (2023)
- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Safe exploration in reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2503.10352/) (2025)
- [Tuning Legged Locomotion Controllers via Safe Bayesian Optimization](https://mlsanity.com/paper/2306.07092/) (2023)
- [PACSBO: Probably approximately correct safe Bayesian optimization](https://mlsanity.com/paper/2409.01163/) (2024)
- [Boundary Exploration for Bayesian Optimization With Unknown Physical Constraints](https://mlsanity.com/paper/2402.07692/) (2024)
- [Koopman-Equivariant Gaussian Processes](https://mlsanity.com/paper/2502.06645/) (2025)
- [Safe Exploration Using Bayesian World Models and Log-Barrier Optimization](https://mlsanity.com/paper/2405.05890/) (2024)
- [Safe Time-Varying Optimization based on Gaussian Processes with Spatio-Temporal Kernel](https://mlsanity.com/paper/2409.18000/) (2024)
- [Towards safe Bayesian optimization with Wiener kernel regression](https://mlsanity.com/paper/2411.02253/) (2024)
- [Safe Bayesian Optimization for the Control of High-Dimensional Embodied Systems](https://mlsanity.com/paper/2412.20350/) (2024)
- [Primal-Dual Contextual Bayesian Optimization for Control System Online Optimization with Time-Average Constraints](https://mlsanity.com/paper/2304.06104/) (2023)
- [A computationally lightweight safe learning algorithm](https://mlsanity.com/paper/2309.03672/) (2023)
- [Local Bayesian Optimization for Controller Tuning with Crash Constraints](https://mlsanity.com/paper/2411.16267/) (2024)
- [Machine Learning Meets Advanced Robotic Manipulation](https://mlsanity.com/paper/2309.12560/) (2023)
- [Efficiently Computable Safety Bounds for Gaussian Processes in Active Learning](https://mlsanity.com/paper/2402.18260/) (2024)
- [Safety and optimality in learning-based control at low computational cost](https://mlsanity.com/paper/2505.08026/) (2025)
- [Benefits of Monotonicity in Safe Exploration with Gaussian Processes](https://mlsanity.com/paper/2211.01561/) (2022)
- [Bayesian inference for data-efficient, explainable, and safe robotic motion planning: A review](https://mlsanity.com/paper/2307.08024/) (2023)
- [Global Safe Sequential Learning via Efficient Knowledge Transfer](https://mlsanity.com/paper/2402.14402/) (2024)
- [Future Aware Safe Active Learning of Time Varying Systems using Gaussian Processes](https://mlsanity.com/paper/2405.10581/) (2024)
- [No-Regret Algorithms for Safe Bayesian Optimization with Monotonicity Constraints](https://mlsanity.com/paper/2406.03264/) (2024)
- [Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review](https://mlsanity.com/paper/2505.07911/) (2025)
- [Safe learning-based control via function-based uncertainty quantification](https://mlsanity.com/paper/2604.01173/) (2026)

## Abstract (arXiv)

When learning policies for robotic systems from data, safety is a major concern, as violation of safety constraints may cause hardware damage. SafeOpt is an efficient Bayesian optimization (BO) algorithm that can learn policies while guaranteeing safety with high probability. However, its search space is limited to an initially given safe region. We extend this method by exploring outside the initial safe area while still guaranteeing safety with high probability. This is achieved by learning a set of initial conditions from which we can recover safely using a learned backup controller in case of a potential failure. We derive conditions for guaranteed convergence to the global optimum and validate GoSafe in hardware experiments.