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

Robotic algorithms typically depend on various parameters, the choice of\nwhich significantly affects the robot's performance. While an initial guess for\nthe parameters may be obtained from dynamic models of the robot, parameters are\nusually tuned manually on the real system to achieve the best performance.\nOptimization algorithms, such as Bayesian optimization, have been used to\nautomate this process. However, these methods may evaluate unsafe parameters\nduring the optimization process that lead to safety-critical system failures.\nRecently, a safe Bayesian optimization algorithm, called SafeOpt, has been\ndeveloped, which guarantees that the performance of the system never falls\nbelow a critical value; that is, safety is defined based on the performance\nfunction. However, coupling performance and safety is often not desirable in\nrobotics. For example, high-gain controllers might achieve low average tracking\nerror (performance), but can overshoot and violate input constraints. In this\npaper, we present a generalized algorithm that allows for multiple safety\nconstraints separate from the objective. Given an initial set of safe\nparameters, the algorithm maximizes performance but only evaluates parameters\nthat satisfy safety for all constraints with high probability. To this end, it\ncarefully explores the parameter space by exploiting regularity assumptions in\nterms of a Gaussian process prior. Moreover, we show how context variables can\nbe used to safely transfer knowledge to new situations and tasks. We provide a\ntheoretical analysis and demonstrate that the proposed algorithm enables fast,\nautomatic, and safe optimization of tuning parameters in experiments on a\nquadrotor vehicle.\n