# How Training Data Impacts Performance in Learning-based Control

arXiv: https://arxiv.org/abs/2005.12062 · HTML: https://mlsanity.com/paper/2005.12062/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2020.

## Built on by (most cited first, 5 of 5)

- [Structure-Preserving Learning Using Gaussian Processes and Variational Integrators](https://mlsanity.com/paper/2112.05451/) (2021)
- [Networked Online Learning for Control of Safety-Critical Resource-Constrained Systems based on Gaussian Processes](https://mlsanity.com/paper/2202.11491/) (2022)
- [Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2208.13006/) (2022)
- [Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning](https://mlsanity.com/paper/2205.15703/) (2022)
- [Event-triggered Control and Online Learning for Networked Systems under Computational Delays](https://mlsanity.com/paper/2608.29576/) (2026)

## Abstract (arXiv)

When first principle models cannot be derived due to the complexity of the real system, data-driven methods allow us to build models from system observations. As these models are employed in learning-based control, the quality of the data plays a crucial role for the performance of the resulting control law. Nevertheless, there hardly exist measures for assessing training data sets, and the impact of the distribution of the data on the closed-loop system properties is largely unknown. This paper derives - based on Gaussian process models - an analytical relationship between the density of the training data and the control performance. We formulate a quality measure for the data set, which we refer to as ρ-gap, and derive the ultimate bound for the tracking error under consideration of the model uncertainty. We show how the ρ-gap can be applied to a feedback linearizing control law and provide numerical illustrations for our approach.