Safe exploration in reproducing kernel Hilbert spaces
This work addresses safety-critical control in reinforcement learning, offering a practical solution for systems where RKHS norm assumptions are typically unknown, though it is incremental in improving existing BO frameworks.
The paper tackles the problem of safe Bayesian optimization (BO) in unknown environments by proposing an algorithm that estimates the RKHS norm from data, enabling improved safety and performance. It demonstrates results on physics simulators and a real inverted pendulum, showing enhanced scalability and safety compared to state-of-the-art methods.
Popular safe Bayesian optimization (BO) algorithms learn control policies for safety-critical systems in unknown environments. However, most algorithms make a smoothness assumption, which is encoded by a known bounded norm in a reproducing kernel Hilbert space (RKHS). The RKHS is a potentially infinite-dimensional space, and it remains unclear how to reliably obtain the RKHS norm of an unknown function. In this work, we propose a safe BO algorithm capable of estimating the RKHS norm from data. We provide statistical guarantees on the RKHS norm estimation, integrate the estimated RKHS norm into existing confidence intervals and show that we retain theoretical guarantees, and prove safety of the resulting safe BO algorithm. We apply our algorithm to safely optimize reinforcement learning policies on physics simulators and on a real inverted pendulum, demonstrating improved performance, safety, and scalability compared to the state-of-the-art.