Robotics 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 parameters during the optimization process that lead to safety-critical system failures. Recently, a safe Bayesian optimization algorithm, called SafeOpt, has been developed and applied in robotics, 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 not desirable in most cases. In this paper, we define separate functions for performance and safety. We present a generalized SafeOpt algorithm that, given an initial safe guess for the parameters, maximizes performance but only evaluates parameters that satisfy all safety constraints with high probability. It achieves this by modeling the underlying and unknown performance and constraint functions as Gaussian processes. We provide a theoretical analysis and demonstrate in experiments on a quadrotor vehicle that the proposed algorithm enables fast, automatic, and safe optimization of tuning parameters. Moreover, we show an extension to context- or environment-dependent, safe optimization in the experiments.

@article{berkenkamp21bayesian,
	author = {Felix Berkenkamp and Andreas Krause and Angela P. Schoellig},
	doi = {https://doi.org/10.1007/s10994-021-06019-1},
	institution = {arXiv},
	journal = {Machine Learning Journal, Special Issue on Robust Machine Learning},
	title = {Bayesian Optimization with Safety Constraints: Safe and Automatic Parameter Tuning in Robotics},
	video = {https://youtu.be/GiqNQdzc5TI},
	year = {2021}}