Online Learning of Parameterized Uncertain Dynamical Environments with Finite-sample Guarantees

TL;DR

This paper introduces an online learning algorithm for uncertain dynamical systems with probabilistic guarantees, capable of adapting to unknown parameters and disturbances, demonstrated on a robot example.

Contribution

It develops a novel probabilistic characterization for systems with unknown mean behavior and disturbances, extending to parameterized environments with online adaptation.

Findings

Probabilistic bounds for systems with additive subGaussian disturbances.

Algorithm adapts to unknown parameters while maintaining guarantees.

Successful application to a differential-drive robot under uncertainty.

Abstract

We present a novel online learning algorithm for a class of unknown and uncertain dynamical environments that are fully observable. First, we obtain a novel probabilistic characterization of systems whose mean behavior is known but which are subject to additive, unknown subGaussian disturbances. This characterization relies on recent concentration of measure results and is given in terms of ambiguity sets. Second, we extend the results to environments whose mean behavior is also unknown but described by a parameterized class of possible mean behaviors. Our algorithm adapts the ambiguity set dynamically by learning the parametric dependence online, and retaining similar probabilistic guarantees with respect to the additive, unknown disturbance. We illustrate the results on a differential-drive robot subject to environmental uncertainty.