Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications
This addresses a key limitation in safety-critical machine learning by enabling robust error quantification without prior hyperparameter bounds, though it is incremental as it builds on existing Gaussian process frameworks.
The paper tackles the problem of Gaussian process error bounds in safety-critical applications when kernel hyperparameters are unknown, introducing a method that computes a confidence region for hyperparameters to derive probabilistic error bounds, with experiments showing it outperforms vanilla and fully Bayesian Gaussian processes.
Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.