How Training Data Impacts Performance in Learning-Based Control

Abstract

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.

The birth of a science

“…Thus, by using the interpretation of Figure 3, it can reveal that some new science was born and the umbilical cord remained attached to mathematics. The term data (plural of datum) has been recognized for a long time (Anonim, 1824;Nasution, Aulia, & Elveny, 2019, Lederer, Capone, Umlauft, & Hirche, 2020. While the presentation of the term data science has so far only in several context of discussion in the last thirty years.…”

AHLS‐pred: a novel sequence‐based predictor of acyl‐homoserine‐lactone synthases using machine learning algorithms

“…It is notable that despite achieving an accuracy of 99.4% in fivefold cross-validation and 94.7% in the independent test as the first machine learning prediction approach for AHLSs, AHLS-pred still faces some In terms of dataset preparation and pre-processing, the quality of the training dataset, to some extent, affects the abilities of the training model. The model trained on highquality, sufficient and balanced datasets will be more robust and will achieve better predictive performance (Lederer et al, 2021). As more and more validated AHLSs data are discovered in the future, the training dataset used in this work will become limited and require expansion.…”

Lessons Learned from Data-Driven Building Control Experiments: Contrasting Gaussian Process-based MPC, Bilevel DeePC, and Deep Reinforcement Learning

“…Whereas the mean function µ(x) plays the role of the nominal dynamics, the variance information var(x) is used to tighten the optimization problem constraints, conferring on it a certain degree of robustness. Although GP-MPC can be extended to incorporate online data in real-time, this feature was not exploited in our experimental investigation since it would bring about both theoretical and computational challenges [29], [30].…”

“…Moreover, even though control performance is heavily influenced by the data quality, it is often difficult to formally measure and quantify this influence, especially in the nonlinear setting (see e.g. [29]). The pragmatic approach is typically to gather 'rich enough' data-sets around different operating points and then rely on different model validation procedures.…”