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

arXiv: https://arxiv.org/abs/2009.02390 · HTML: https://mlsanity.com/paper/2009.02390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [Online Optimization and Ambiguity-based Learning of Distributionally Uncertain Dynamic Systems](https://mlsanity.com/paper/2102.09111/) (2021)

## Abstract (arXiv)

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.