Uniform Error Bounds for Gaussian Process Regression with Application to Safe Control
This work addresses the need for reliable error bounds in data-driven models for safe control applications, representing an incremental improvement over prior restrictive assumptions.
The paper tackles the problem of quantifying model errors in Gaussian process regression for safety-critical control by deriving a novel uniform error bound under weaker assumptions than existing methods, and demonstrates its application in simulations of a robotic manipulator.
Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure and uniform error bounds have been derived, which allow safe control based on these models. However, existing error bounds require restrictive assumptions. In this paper, we employ the Gaussian process distribution and continuity arguments to derive a novel uniform error bound under weaker assumptions. Furthermore, we demonstrate how this distribution can be used to derive probabilistic Lipschitz constants and analyze the asymptotic behavior of our bound. Finally, we derive safety conditions for the control of unknown dynamical systems based on Gaussian process models and evaluate them in simulations of a robotic manipulator.