Bayesian optimization with safety constraints: safe and automatic parameter tuning in robotics.

Selecting the right tuning parameters for algorithms is a pravelent problem in machine learning that can significantly affect the performance of algorithms. Data-efficient optimization algorithms, such as Bayesian optimization, have been used to automate this process. During experiments on real-world systems such as robotic platforms these methods can evaluate unsafe parameters that lead to safety-critical system failures and can destroy the system. 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 practice, since they are often opposing objectives. 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.