Safe learning-based control via function-based uncertainty quantification

TL;DR

This paper introduces a novel method for uncertainty quantification in learning-based control, using scenario approach-based uncertainty tubes that require minimal assumptions and are applicable to discontinuous functions.

Contribution

It proposes a new approach to construct uncertainty tubes from sampled realizations, enabling safer control tuning without restrictive assumptions.

Findings

Successfully applied to tuning control parameters on a real Furuta pendulum.

Constructed high-probability uncertainty tubes using only sampled realizations.

Enhanced safety and robustness in learning-based control systems.

Abstract

Uncertainty quantification is essential when deploying learning-based control methods in safety-critical systems. This is commonly realized by constructing uncertainty tubes that enclose the unknown function of interest, e.g., the reward and constraint functions or the underlying dynamics model, with high probability. However, existing approaches for uncertainty quantification typically rely on restrictive assumptions on the unknown function, such as known bounds on functional norms or Lipschitz constants, and struggle with discontinuities. In this paper, we model the unknown function as a random function from which independent and identically distributed realizations can be generated, and construct uncertainty tubes via the scenario approach that hold with high probability and rely solely on the sampled realizations. We integrate these uncertainty tubes into a safe Bayesian optimization algorithm, which we then use to safely tune control parameters on a real Furuta pendulum.