Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression
This work addresses the need for reliable uncertainty estimates in safety-critical domains such as learning-based control, offering a solution that balances theoretical rigor with practical applicability, though it is incremental in improving existing bounds.
The paper tackles the problem of overly conservative frequentist uncertainty bounds in Gaussian Process Regression, which are needed for safety-critical applications like learning-based control, by introducing new bounds that are rigorous, practically useful, and less conservative than state-of-the-art results, as demonstrated with numerical examples.
Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important applications, like learning-based control with safety guarantees, frequentist uncertainty bounds are required. Although such rigorous bounds are available for Gaussian Processes, they are too conservative to be useful in applications. This often leads practitioners to replacing these bounds by heuristics, thus breaking all theoretical guarantees. To address this problem, we introduce new uncertainty bounds that are rigorous, yet practically useful at the same time. In particular, the bounds can be explicitly evaluated and are much less conservative than state of the art results. Furthermore, we show that certain model misspecifications lead to only graceful degradation. We demonstrate these advantages and the usefulness of our results for learning-based control with numerical examples.